Answer:
The 85% confidence interval is ( 7.7 , 8.0 )
Step-by-step explanation:
In order to find the 85% confidence interval you use the following formula:
[tex]\overline{x}\pm Z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
where
[tex]\overline{x}[/tex]: mean of number of bacteria reproduces per hour = 7.8
σ: standard deviation = 2.2
n: sample size = 967
α: 1 - 0.85 = 0.15
Zα/2: Z factor of the density distribution = 1.44
You replace the values of all parameters in the equation (1):
[tex]7.8\pm (1.44)\frac{2.2}{\sqrt{697}}\\\\7.8\pm0.119\\\\[/tex]
Then, the confidence interval is:
[tex](7.8-0.119,7.8+0.119)\\\\(7.7,8.0)[/tex]
An HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells you that the printing speed is actually a Normal random variable with a mean of 17.35 ppm and a standard deviation of 3.25 ppm. Suppose that you draw a random sample of 10 printers.
Required:
a. Using the information about the distribution of the printing speeds given by the manufacturer, find the probability that the mean printing speed of the sample is greater than 17.55 ppm.
b. Use normal approximation to find the probability that more than 48.6% of the sampled printers operate at the advertised speed (i.e. the printing speed is equal to or greater than 18 ppm)
Answer:
a) The probability that the mean printing speed of the sample is greater than 17.55 ppm = 0.4247
b) The probability that more than 48.6% of the sampled printers operate at the advertised speed = 0.4197
Step-by-step explanation:
The central limit theorem explains that for an independent random sample, the mean of the sampling distribution is approximately equal to the population mean and the standard deviation of the distribution of sample is given as
σₓ = (σ/√n)
where σ = population standard deviation
n = sample size
So,
Mean of the distribution of samples = population mean
μₓ = μ = 17.35 ppm
σₓ = (σ/√n) = (3.25/√10) = 1.028 ppm
a) The probability that the mean printing speed of the sample is greater than 17.55 ppm.
P(x > 17 55)
We first normalize 17.55 ppm
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (17.55 - 17.35)/1.028 = 0.19
To determine the required probability
P(x > 17.55) = P(z > 0.19)
We'll use data from the normal probability table for these probabilities
P(x > 17.55) = P(z > 0.19) = 1 - P(z ≤ 0.19)
= 1 - 0.57535 = 0.42465 = 0.4247
b) The probability that more than 48.6% of the sampled printers operate at the advertised speed
We first find the probability that one randomly selected printer operates at the advertised speed.
Mean = 17.35 ppm
Standard deviation = 3.25 ppm
Advertised speed = 18 ppm
Required probability = P(x ≥ 18)
We standardize 18 ppm
z = (x - μ)/σ = (18 - 17.35)/3.25 = 0.20
To determine the required probability
P(x ≥ 18) = P(z ≥ 0.20)
We'll use data from the normal probability table for these probabilities
P(x ≥ 18) = P(z ≥ 0.20) = 1 - P(z < 0.20)
= 1 - 0.57926 = 0.42074
48.6% of the sample = 48.6% × 10 = 4.86
Greater than 4.86 printers out of 10 includes 5 upwards.
Probability that one printer operates at advertised speed = 0.42074
Probability that one printer does not operate at advertised speed = 1 - 0.42074 = 0.57926
probability that more than 48.6% of the sampled printers operate at the advertised speed will be obtained using binomial distribution formula since a binomial experiment is one in which the probability of success doesn't change with every run or number of trials. It usually consists of a number of runs/trials with only two possible outcomes, a success or a failure. The outcome of each trial/run of a binomial experiment is independent of one another.
Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = 10
x = Number of successes required = greater than 4.86, that is, 5, 6, 7, 8, 9 and 10
p = probability of success = 0.42074
q = probability of failure = 0.57926
P(X > 4.86) = P(X ≥ 5) = P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9) + P(X=10) = 0.4196798909 = 0.4197
Hope this Helps!!!
Nike sells 20,000 pairs of shoes for $200 each pair. How much revenue did Nike make?
Answer:
$4,000,000
Step-by-step explanation:
20,000*200=4,000,000
Dora likes to explore. Recently, she explored southeast Australia where she found some very large trees known as Eucalyptus regnans or Mountain Ash. She wondered if they were taller, on average, than the coastal Douglas Firs of her native state of Oregon in the United States, which have an average height of 250 feet in old growth areas. Dora measured the heights of 15 Mountain Ash trees in southeast Australia and found an average height of these trees of 293 feet. Suppose s 25 feet. Assume the heights of the 15 trees in Dora's sample are representative of the heights of all Mountain Ash trees in southeast Australia. The t-statistic for this problem is 6.661. Based on this t-statistic, which of the following is true? Choose the correct answer below.
A. With a p-value of 0.999, there is sufficient evidence to accept the null hypothesis as true.
B. With a p-value less than 0.0001, there is not sufficient evidence to reject the null hypothesis and accept the alternative as true. y
C. With a p-value less than 0.0001, there is sufficient evidence to reject the null hypothesis and accept the alternative as true.
D. With a p-value less than 0.0001, there is not sufficient evidence to accept the null hypothesis as true. 0 E. With a p-value of 0.999, there is not sufficient evidence to reject the null hypothesis and accept the alternative as true.
Answer:
C. With a p-value less than 0.0001, there is sufficient evidence to reject the null hypothesis and accept the alternative as true.
Step-by-step explanation:
She performed an hypothesis test with the sample of size n=15 that she takes. The t-statistic has a value of 6.661.
The degrees of freedom for this sample size are:
[tex]df=n-1=15-1=14[/tex]
The P-value for a statistic t=6.661 and 14 degrees of freedom is:
[tex]\text{P-value}=P(t>6.661)=0.00001[/tex]
With these P-value we know that the effect is significant and the null hypothesis is rejected. There is enough evidence to support the claim that the mean height of Mountain Ash trees is greater than the coastal Douglas Firs.
To prove a polygon is a rectangle which of the properties listed must be included in the proof
Answer:
if the diagonals of a parallelogram are congruent, then it's a rectangle (neither the reverse of the definition nor the converse of a property). If a parallelogram contains a right angle, then it's a rectangle (neither the reverse of the definition nor the converse of a property).
Step-by-step explanation:
You are choosing between two different window washing companies. The first charges $5 per window. The second charges a base fee of $40 plus $3 per window
Answer:
you forgot the rest of the question homie but once there is 20 companies both companies will be equal
Step-by-step explanation:
Answer:
20 windows
Step-by-step explanation:
Find the function value. tan495°
Answer: -1
Step-by-step explanation:
You want to find an angle that is coterminal to 495. So, subtract 360 degrees until youre in the range of 0-360. I got 495 - 360 = 135°
Tangent is equal to [tex]\frac{sin(theta)}{cos(theta)}[/tex], we already solved theta which was 135°
This next part is hard to explain to someone who doesnt know their trig circle, idk if you do. The angle 135 is apart of the pi/4 gang. So we know this is going to be some variant of √2/2. Sine of quadrant 1 and 2 is gonna be positive:
[tex]sin135=\frac{\sqrt{2} }{2}[/tex]
Now lets do cosine of 135°, which again is apart of the pi/4 gang because its divisible by 45°. Its in quadrant 2 so the cosine will be negative.
[tex]cos135=-\frac{\sqrt{2} }{2}[/tex]
The final step is to divide them. They are both fractions so you should multiply by the reciprocal.
[tex]\frac{\sqrt{2} }{2} *-\frac{2}{\sqrt{2} } =-\frac{2\sqrt{2} }{2\sqrt{2} } =-1[/tex]
The HCF of two numbers is 11, and their L.C.M is 368. If one number is 64, then the other number is ….
Answer:
63.45
Step-by-step explanation:
First, it should be noted that the question is incorrect because 64 can't be divided by 11 but assuming that the question is correct, the solution is as follows
Given
LCM = 368
HCF = 11
One number = 64
Required
The other number
Let both numbers be represented by m and n, such that
[tex]m = 64[/tex]
From laws of HCF and LCM
The product of both numbers = Product of HCF and LCM
i.e.
[tex]m * n = HCF * LCM[/tex]
By substituting 68 for m; 368 for LCM and 11 for HCF
[tex]m * n = HCF * LCM[/tex] becomes
[tex]64 * n = 368 * 11[/tex]
[tex]64n = 4048[/tex]
Divide both sides by 64
[tex]\frac{64n}{64} = \frac{4048}{64}[/tex]
[tex]n = \frac{4048}{64}[/tex]
[tex]n = 63.25[/tex]
which of the following is equal to? WILL GIVE BRAINLIST
Answer:
the third answer i am pretty sure because my brother is learning this and he told me and he has As
Step-by-step explanation:
if yo need any more help please tell me please mark as brainliest i only got it twice
PLEASE HELP
In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x2 to the number of x-intercepts in the graph of g(x) = (x-2)2 -3. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).
Answer:
Ok, for f(x) = x^2 we have only one x-intercept (actually, two equal x-intercepts) at x = 0.
Now, for g(x) = (x - 2)^2 - 3
First, let's analyze the transformations.
When we have g(x) = f(x - a) this means that we moved "a" units to the right (if a is positive)
When we have g(x) = f(x) + a, this means that (if a > 0) we move the graph "a" units up.
In this case we have both those transformations:
g(x) = f(x - 2) - 3
this means that we move 2 units to the right, and 3 units down (because the number is negative)
now we can find the roots of g(x) as:
g(x) = (x - 2)^2 - 3 = x^2 - 4x + 4 - 3 = x^2 - 4x + 1 = 0
using the Bhaskara's equation:
[tex]x = \frac{4 +-\sqrt{4^2 - 4*1*1} }{2*1} = \frac{4 +- 3.5}{2}[/tex]
then the roots are:
x = (4 + 3.5)/2 = 3.75
x = (4 - 3.5)/2 = 0.25
Here we have two different x-intercepts
how do i know when a set of ordered pairs that represents a function?
Answer:
How do you figure out if a relation is a function? You could set up the relation as a table of ordered pairs. Then, test to see if each element in the domain is matched with exactly one element in the range. If so, you have a function!
Step-by-step explanation:
Which whole number can each term of the equation be multiplied by to eliminate the fractions before solving
Answer:
the least common denominator
Step-by-step explanation:
The least common denominator is that number. It is the least common multiple of the denominator values.
__
Simply multiplying by the product of the denominators will eliminate fractions, but may require reduction of fractions in the answer. If the "fractions" are rational expressions, extraneous solutions may be introduced.
Suppose you want to buy a new car and are trying to choose between two models: Model A: costs $16,500 and its gas mileage is 25 miles per gallon and its insurance is $250 per year. Model B: costs $24,500 and its gas mileage is 40 miles per gallon and its insurance is $450 per year. If you drive approximately 40,000 miles per year and the gas costs $3 per gallon:
1. Find a formula for the total cost of owning Model A where the number of years you own the car is represented by x.
2. Find a formula for the total cost of owning Model B where the number of years is the independent variable.
3. Find the total cost for each model for the first five years. If you plan to keep the car for 4 years, which model is more economical?
4. Find the number of years in which the total cost to keep the two cars will be the same.
5. Identify the number of months where neither car holds a cost of ownership advantage.
6. What effect would the cost of gas doubling have on cost of ownership?
7. If you can sell neither car for 40% of its value at any time, how does the analysis change?
Answer:
1. CA=16,500+5,050x
2. CB=24,500+3,450x
3. CA(x=5)=CB(x=5)=41,750
If keeped 4 years, Model A is more economical.
4. 5 years
5. From month 49 to 61.
6. The cost of ownership of Model A increases more than Model B, as it is less gas efficient. The break-even point for x is reduced from x=5 to x=2.35.
7. The fixed cost are reduced by a 40%, so the variable cost, the ones that depend on time of ownership, are increased in importance.
Step-by-step explanation:
We can express the cost of ownership as the sum of the purchase cost, gas cost and insurance cost.
1. For model A we have:
[tex]\text{Cost of ownership}=\text{Purchase cost}+\text{Gas cost}+\text{Insurance cost}\\\\\text{Cost of ownership}=\$16,500+3 \dfrac{\$}{gal}\cdot\dfrac{1\,gal}{25\,miles}\cdot \dfrac{40,000\,miles}{year}\cdot x+\$250\cdot x\\\\\\\text{Cost of ownership}=\$16,500+\$4,800x+\$250x\\\\\\\text{Cost of ownership}=$16,500+\$5,050x[/tex]
2. For model B we have:
[tex]\text{Cost of ownership}=\text{Purchase cost}+\text{Gas cost}+\text{Insurance cost}\\\\\text{Cost of ownership}=\$24,500+3 \dfrac{\$}{gal}\cdot\dfrac{1\,gal}{40\,miles}\cdot \dfrac{40,000\,miles}{year}\cdot x+\$450\cdot x\\\\\\\text{Cost of ownership}=\$24,500+\$3,000x+\$450x\\\\\\\text{Cost of ownership}=$24,500+\$3,450x[/tex]
3. If x=5, the costs for each car are:
[tex]\text{CoOwn A}=16,500+5,050\cdot(5)=16,500+25,250=41,750\\\\\\\text{CoOwn B}=24,500+3,450\cdot(5)=24,500+17,250=41,750[/tex]
5 years is the break-even point for the cost of ownership between these two cars.
If you plan to keep the car for 4 years, the costs are:
[tex]\text{CoOwn A}=16,500+5,050\cdot(4)=16,500+20,200=36,700\\\\\\\text{CoOwn B}=24,500+3,450\cdot(4)=24,500+13,800=38,300[/tex]
For a 4 year period ownership, the model A is more economical ($36,700).
4. This happens for 1 year, the fifth year, in which the two models have the same cost of ownership.
5. At the 5th year, the cost for both models are the same.
Then, this corresponds to the months 4*12+1=48+1=49 and 5*12+1=61.
6. If the cost of gas doubles, the cost of ownership would rise for both model, but more for the Model A, which is less gas efficient and hence has a higher gas cost.
Model A
[tex]\text{Cost of ownership}=\text{Purchase cost}+\text{Gas cost}+\text{Insurance cost}\\\\\text{Cost of ownership}=\$16,500+6 \dfrac{\$}{gal}\cdot\dfrac{1\,gal}{25\,miles}\cdot \dfrac{40,000\,miles}{year}\cdot x+\$250\cdot x\\\\\\\text{Cost of ownership}=\$16,500+\$9,600x+\$250x\\\\\\\text{Cost of ownership}=$16,500+\$9,850x[/tex]
Model B
[tex]\text{Cost of ownership}=\text{Purchase cost}+\text{Gas cost}+\text{Insurance cost}\\\\\text{Cost of ownership}=\$24,500+6 \dfrac{\$}{gal}\cdot\dfrac{1\,gal}{40\,miles}\cdot \dfrac{40,000\,miles}{year}\cdot x+\$450\cdot x\\\\\\\text{Cost of ownership}=\$24,500+\$6,000x+\$450x\\\\\\\text{Cost of ownership}=$24,500+\$6,450x[/tex]
The breakeven point goes from x=5 (for $3 per gallon) to x=2.35 (for $6 per gallon).
[tex]16,500+9,850x=24,500+6,450x\\\\(9,850-6,450)x=24,500-16,500\\\\x=8,000/3400=2.35[/tex]
7. If we can sell any car for 40% of its value at any time, the cost of ownership becames:
Model A:
[tex]\text{Cost of ownership}=16,500+5,050x-0.4\cdot16,500\\\\\text{Cost of ownership}=9,900+5,050x[/tex]
Model B
[tex]\text{Cost of ownership}=24,500+3,450x-0.4\cdot24,500\\\\\text{Cost of ownership}=14,700+3,450x[/tex]
The fixed costs are lowered by 40%, so the variable costs (the ones that depend on time) became more important.
Zia is building a plastic model rocket that has the combined shape of a cone and a cylinder as shown. additionally, the cylinder has a hemisphere hollowed out of its bottom. the plastic for the cone weighs 1.4 grams per cubic centimeter and the plastic for the cylinder weights only 0.8 grams per cubic centimeter.
(a) the volume of plastic that remains in the cylinder after it has been hollowed out to the nearest cubic centimeter.
(b) what has a greater total weight, the plastic that makes up the cone or the plastic that makes up the cylinder after it has been hollowed out?
Answer:
226 cm^3
The mass of plastic used to make cylinder is greater
Step-by-step explanation:
Given:-
- The density of cone material, ρc = 1.4 g / cm^3
- The density of cylinder material, ρl = 0.8 g / cm^3
Solution:-
- To determine the volume of plastic that remains in the cylinder after gouging out a hemispherical amount of material.
- We will first consider a solid cylinder with length ( L = 10 cm ) and diameter ( d = 6 cm ). The volume of a cylinder is expressed as follows:
[tex]V_L =\pi \frac{d^2}{4} * L[/tex]
- Determine the volume of complete cylindrical body as follows:
[tex]V_L = \pi \frac{(6)^2}{4} * 10\\\\V_L = 90\pi cm^3\\[/tex]
- Where the volume of hemisphere with diameter ( d = 6 cm ) is given by:
[tex]V_h = \frac{\pi }{12}*d^3[/tex]
- Determine the volume of hemisphere gouged out as follows:
[tex]V_h = \frac{\pi }{12}*6^3\\\\V_h = 18\pi cm^3[/tex]
- Apply the principle of super-position and subtract the volume of hemisphere from the cylinder as follows to the nearest ( cm^3 ):
[tex]V = V_L - V_h\\\\V = 90\pi - 18\pi \\\\V = 226 cm^3[/tex]
Answer: The amount of volume that remains in the cylinder is 226 cm^3
- The volume of cone with base diameter ( d = 6 cm ) and height ( h = 5 cm ) is expressed as follows:
[tex]V_c = \frac{\pi }{12} *d^2 * h[/tex]
- Determine the volume of cone:
[tex]V_c = \frac{\pi }{12} *6^2 * 5\\\\V_c = 15\pi cm^3[/tex]
- The mass of plastic for the cylinder and the cone can be evaluated using their respective densities and volumes as follows:
[tex]m_i = p_i * V_i[/tex]
- The mass of plastic used to make the cylinder ( after removing hemispherical amount ) is:
[tex]m_L = p_L * V\\\\m_L = 0.8 * 226\\\\m_L = 180.8 g[/tex]
- Similarly the mass of plastic used to make the cone would be:
[tex]m_c = p_c * V_c\\\\m_c = 1.4 * 15\pi \\\\m_c = 65.973 g[/tex]
Answer: The total weight of the cylinder ( m_l = 180.8 g ) is greater than the total weight of the cone ( m_c = 66 g ).
The volume of the remaining plastic in the cylinder is large, which
makes the weight much larger than the weight of the cone.
Responses:
(a) Volume of the remaining plastic in the cylinder is 226 cm³(b) The weight of the cylinder is greater than the weight of the cone.How can the weight and volume be evaluated?Density of the plastic for the cone = 1.4 g/cm³
Density of the plastic used for the cylinder = 0.8 g/cm³
From a similar question, we have;
Height of the cylinder = 10 cm
Diameter of the cylinder = 6 cm
Height of the cone = 5 cm
(a) Radius of the cylinder, r = 6 cm ÷ 2 = 3 cm
Volume of a cylinder = π·r²·h
Volume of a hemisphere = [tex]\mathbf{\frac{2}{3}}[/tex] × π× r³
Volume of the cylinder after it has been hollowed out, V, is therefore;
[tex]V = \mathbf{\pi \times r^2 \times h - \frac{2}{3} \times \pi \times r^3}[/tex]Which gives;
[tex]V = \pi \times 3^2 \times 10 - \frac{2}{3} \times \pi \times 3^3 \approx \mathbf{ 226}[/tex]
Volume of the cylinder after it has been hollowed out, V ≈ 226 cm³(b) Volume of the cone = [tex]\mathbf{\frac{1}{3}}[/tex] × π × 3² × 5 ≈ 47.1
Mass of the cone = 47.1 cm³ × 1.4 g/cm³ ≈ 66 g
Mass of the hollowed cylinder ≈ 226 cm³ × 0.8 g/cm³ = 180.8 g
The mass and therefore, the weight of the plastic that makes up the hollowed cylinder is greater than the weight of the plastic that makes up the cone.Learn more about volume and density of solids here:
https://brainly.com/question/4773953
A new post-surgical treatment is being compared with a standard treatment. Seven subjects receive the new treatment, while seven others (the controls) receive the standard treatment. The recovery times, in days, are given below.
Treatment: 12 13 15 19 20 21 24
Control: 18 23 24 30 32 35 39
Required:
Find a 98% confidence interval for the difference in the mean recovery times between treatment and control.
Answer:
[tex] (17.714-28.714) -2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -19.745[/tex]
[tex] (17.714-28.714) +2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -2.255[/tex]
Step-by-step explanation:
For this case we have the following info given:
Treatment: 12 13 15 19 20 21 24
Control: 18 23 24 30 32 35 39
We can find the sample mean and deviations with the the following formulas:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex] s =\sqrt{\frac{\sum_{i=1}^n (X_i- \bar X)^2}{n-1}}[/tex]
And repaplacing we got:
[tex] \bar X_T = 17.714[/tex] the sample mean for treatment
[tex] \bar X_C = 28.714[/tex] the sample mean for treatment
[tex] s_T= 4.461[/tex] the sample deviation for treatment
[tex] s_C= 7.387[/tex] the sample deviation for control
[tex]n_T= n_C= 7[/tex] the sample size for each sample
The degrees of freedom are given by:
[tex] df= 7+7-2= 12[/tex]
The confidence interval for the difference of means is given by:
[tex] (\bar X_T -\bar X_C) \pm t_{\alpha/2} \sqrt{\frac{s^2_T}{n_T} +\frac{s^2_C}{n_C}}[/tex]
The confidence is 98% so then the significance is [tex]\alpha=0.02[/tex] and [tex] \alpha/2 =0.01[/tex]. Then the critical value would be:
[tex] t_{\alpha/2}=2.681[/tex]
And replacing we got:
[tex] (17.714-28.714) -2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -19.745[/tex]
[tex] (17.714-28.714) +2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -2.255[/tex]
Lisa washes dishes at the local diner. She can wash 4 dishes every minute. What is the algebraic equation to express the function of the total number of dishes Lisa washes?
Answer:
f(x)= 4x or y=4x
Step-by-step explanation:
X represents minutes and the 4 is how many dishes she can wash.
Arlene sleeps for 7hr20min each night. How many hours does she sleep in a week? Write your answer as a mixed number,
Answer:
51 1/3 hours
Step-by-step explanation:
Multiply the amount of sleep per day (7 1/3) by the number of days in a week (7), to get the total amount of sleep (51 1/3 hours)
A) Divide 160km in the ratio 10:9:13
B) divide 66 in the ratio 6:15:1
Answer:
A) 50 km : 45 km : 65 km
B) 18:45:3
Step-by-step explanation:
A) 160 km in the ratio 10:9:13
10x+9x+13x= 16032x= 160x= 510:9:3 ⇔ 50 km : 45 km : 65 km
B) 66 in the ratio 6:15:1
6x+15x+x= 6622x=66x=36:15:1 ⇔ 18:45:3
Please help . I’ll mark you as brainliest if correct! Only the one marked with an X is wrong . I don’t get it
Answer:
(x+7)² = 9
Step-by-step explanation:
x² + 14x + 40 = 0
(x² + 14x) + 40 = 0
(x² +14x +49) + 40 - 49 = 0
(x+7)² - 9 = 0
(x+7)² = 9
Hope this helps!
Answer:
(x+7)² = 9
Step-by-step explanation:
The equation 9(u – 2) + 1.5u = 8.25 models the total miles Michael traveled one afternoon while sledding, where u equals the number of hours walking up a hill and (u – 2) equals the number of hours sledding down the hill. Which is the value of u?
Answer:
2.5
Step-by-step explanation:
[tex]9(u-2)+1.5u=8.25 \\\\9u-18+1.5u=8.25\\\\10.5u-18=8.25\\\\10.5u=26.25\\\\u=2.5[/tex]
Hope this helps!
Chrissy currently has a credit card that charges 15% interest. She usually carries a balance of about $500. What will her total annual interest be with her current card?
Answer:
$900
Step-by-step explanation:
If she holds $500 and she is charged 15%; it means
The interest she pays per month is ;
$500 × 15/100 = $75
Then annually meaning for 12 months, she pays;
$75 × 12 = $900
Her annual interest on her current card is $900.
How to calculate annual interest?The annual percentage rate (APR) is the interest generated by a sum charged to borrowers or paid to investors each year. The annual percentage rate (APR) is a percentage that represents the actual annual cost of funds over the life of a loan or the income earned on an investment.Your daily periodic interest is calculated by dividing your annual percentage rate (APR) by the number of days in the year, which is typically 360 or 365 days depending on your credit card issuer. The annual interest rate is the rate that is applied over a one-year period.Therefore,
She will be taxed 15% if she holds $500, which means
The monthly interest she pays is;
$500 × 15/100 = $75
She then pays annually, which is for a full year;
$75 × 12 = $900
Hence, Her annual interest on her current card is $900.
To learn more about annual interest refer to:
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The area of a circle is 18 pi square inches. If the area of a sector of this circle is 6 pi square inches, then
which of the following must be the sector's central angle?
Answer:
120°Step-by-step explanation:
Area of a sector = [tex]\frac{\theta}{360} * \pi r^{2}\ where\ \pi r^{2} \ is\ the\ area\ of\ the\ circle[/tex]
theta is the sector's central angle
Area of the sector = [tex]\frac{\theta}{360} * \ area\ of\ a\ circle[/tex]
Given area of a circle = 18πin² and area of a sector = 6πin²
On substituting;
6π = [tex]\theta/360 * 18 \pi[/tex]
Dividing both sides by 18π we have;
1/3 = [tex]\theta/360[/tex]
[tex]3 \theta = 360\\\theta = 360/3\\\theta = 120^{0}[/tex]
The sector's central angle is 120°
Question 6: An experiment consists of throwing two six-sided dice and observing the number of spots on the upper faces. Determine the probability that (a) each die shows four or more spots. (b) the sum of the spots is not 3. (c) neither a one nor a six appear on each die. (d) the sum of the spots is 7
Answer:
(a) 0.25
(b) 0.944
(c) 0.444
(d) 0.167
Step-by-step explanation:
There are six possible outcomes for each die, which means that the number of possible outcomes is:
[tex]n=6*6 = 36[/tex]
(a) In order for each die to show four or more spots they will both have to land on a four, five or six. The probability of this happening is:
[tex]P(A) = \frac{3*3}{36}=0.25[/tex]
(b) There are only two possible outcomes for which the sum is three (1 and 2, or 2 and 1). The probability of the sum NOT being three is:
[tex]P(B) = 1-\frac{2}{36}=0.944[/tex]
(c) If neither a one or a six must appear, then there are 4 possible outcomes for each die, the probability is:
[tex]P(C) = \frac{4*4}{36}=0.444[/tex]
(d) For each one of the six possible numbers on the first die, there is only one on the second die for which the sum of the spots is 7, totaling six possible ways to sum 7:
[tex]P(D) = \frac{6}{36}=0.167[/tex]
The required probability output from a throw of two six sided dice are as follows :
0.25 0.9440.4440.167The sample space for two throw of a six-sided die :
Sample space = n² = 6² = 6 × 6 = 36Recall :
Probability = required outcome / Total possible outcomesA.) Obtaining 4 or more spots :
Required spot = (5, 6, 7) on each die = 3 × 3 = 9 outcomes
P(4 or more spot) = 9/36 = 0.25
B.) Sum of spot is not 3 :
Sum of spot = 3 ; (1, 2) and (2, 1) = 2 possible outcomes
P(sum not 3) = 1 - (2/36) = 1 - 1/8 = 17/18 = 0.944
C.) neither a one nor 6 appears :
Required = (2, 3, 4, 5) = 4 × 4 = 16
P(neither 6 nor 1) = 16/36 = 4/9 = 0.44
D.) Sum of spot equals 7
Required = (1, 6),(6,1),(5,2),(2,5),(3,4),(4,3) = 6 outcomes
P(sum equals 7) = 6/36 = 1/6 = 0.167
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What is an equation of a line, in point-slope form, that
passes through (1, – 7) and has a slope of -2/3
y-7= }(1-1)
y+7= (1+1)
y-7=-|(+1)
y+7=-3(2-1)
Answer:
y + 7 = -2/3 (x - 1)
Step-by-step explanation:
Point-slope form is y - y1 = m (x - x1)
-7 is y1, -2/3 is m, and 1 is x1
When you plug the values in, you get y + 7 = -2/3 (x - 1)
Mathematics
ose the correct answer:
. What number should be added to (-5/16) to get ( 7/24)?
Answer:
0.6042 or 29/48
Step-by-step explanation:
-5/16 = -0.3125
7/24 = 0.2917
0.2917 - -0.3125 = 0.6042
0.6042 ≅ 29/48
Answer:
29/48
Step-by-step explanation:
-5/16 + x= 7/24
x= 7/24-(-5/16)
x=7/24+5/16
x= 2*7/2*24+ 3*5/3*16
x=29/48
Abena travelled 40% of the distance of her trip alone, went another 35 miles with Saralyn,
and then finished the last half of the journey alone. How many miles long was the journey?
Answer:
350 miles long.
Step-by-step explanation:
First, we analyze the breakdown of the journey
Abena travelled 40% of the distance of her trip alone.She went 35 miles with Saralyn.She finished the last half (50%) of the journey alone.Let the total distance of the journey =x
Therefore:
10% of the total distance of the journey =35 miles
10% of x=35
0.1x=35
Divide both sides by 0.1
x-350 miles
Therefore, the journey was 350 miles long.
Answer:
The journey was 350 miles long
Step-by-step explanation:
The parameters given are;
Distance traveled by Abena alone = 40% and the last half
∴ Distance traveled by Abena alone = 40% + 50% = 90%
Distance Abena traveled with Saralyn = 35 miles = 100% - 90% = 10%
Hence 10% of Abena's journey = 35 miles
The total distance of Abena's journey therefore, is given as follows
10% = 35 miles
Total distance of Abena's journey = 100% of Abena's journey = 10 × 10%
10 × 10% = 10 × 35 miles = 350 miles
The total distance of Abena's journey = 350 miles.
You are on a TV show. You have been asked to either play a dice game five times or accept a $50 bill. The dice game works like this. If you roll a 1, 2 or 3, you win $50. If you roll a 4 or 5, you lose $20. If you roll a 6, you lose $90.
EV= $
Step-by-step explanation:
Take the $50 and quit.
(Each game as outlined by drwls has an expected value of $1.50.
You are playing it 5 times, so the expected return is $7.50.
Your choice was to either accept $50 or play the game)
As a birthday gift, you are mailing a new personal digital assistant (PDA) to your cousin in Toledo. The PDA cost $414. There is a 3 percent chance it will be lost or damaged in the mail. Is it worth $4 to insure the mailing?Explain, using the concept of expected value.
Answer:
It is worth $4 to insure the mailing.
Step-by-step explanation:
The random variable X can be defined as the money value.
The PDA costs, $414.
It is provided that there is a 3% chance it will be lost or damaged in the mail.
So, there is 97% chance it will not be lost or damaged in the mail.
The insurance costs $4.
If the PDA is lost or damaged in the mail when there is no insurance the money value would be of -$414.
And if the PDA is lost or damaged in the mail when there is an insurance the money value would be of $414 - $4 = $410.
Compute the expected value of money as follows:
[tex]\text{E (X)}=(0.97\times 410)+(0.03\times -414)[/tex]
[tex]=397.7-12.42\\=385.28[/tex]
The expected value of money in case the PDA is lost or damaged in the mail or not is $385.28.
Thus, it is worth $4 to insure the mailing.
Many students brag that they have more than 150 friends on a social media website. For a class project, a group of students asked a random sample of 13 students at their college who used the social media website about their number of friends and got the data available below. Is there strong evidence that the mean number of friends for the student population at the college who use the social media website is larger than 150?
Required:
a. Find and interpret the test statistic value.
b. Report and interpret the P-value and state the conclusion in context. Use a significance level of 0.05.
c. What does the test statistic value represent?
1. The test statistic value is the difference between the sample mean and the null hypothesis value.
2. The test statistic value is the number of standard errors from the null hypothesis value to the sample mean.
3. The test statistic value is the expected mean of the differences between the sample data and the null hypothesis value.
4. The test statistic value is the number of standard deviations from the null hypothesis value to the sample mean.
Answer:
Step-by-step explanation:
The question is incomplete. The missing data is:
30, 155, 205, 235, 180, 235, 70, 250, 135, 145, 225, 230, 30
Solution:
Mean = (30 + 155 + 205 + 235 + 180 + 235 + 70 + 250 + 135 + 145 + 225 + 230 + 30)/13 = 163.5
Standard deviation = √(summation(x - mean)²/n
n = 13
Summation(x - mean)² = (30 - 163.5)^2 + (155 - 163.5)^2 + (205 - 163.5)^2+ (235 - 163.5)^2 + (180 - 163.5)^2 + (235 - 163.5)^2 + (70 - 163.5)^2 + (250 - 163.5)^2 + (135 - 163.5)^2 + (145 - 163.5)^2 + (225 - 163.5)^2 + (230 - 163.5)^2 + (30 - 163.5)^2 = 73519.25
Standard deviation = √(73519.25/13) = 75.2
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ ≤ 150
For the alternative hypothesis,
µ > 150
It is a right tailed test.
a) Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 13,
Degrees of freedom, df = n - 1 = 13 - 1 = 12
t = (x - µ)/(s/√n)
Where
x = sample mean = 163.5
µ = population mean = 150
s = samples standard deviation = 75.2
t = (163.5 - 150)/(75.2/√13) = 0.65
The lower the test statistic value, the higher the p value and the higher the possibility of accepting the null hypothesis.
b) We would determine the p value using the t test calculator. It becomes
p = 0.26
Since alpha, 0.05 < than the p value, 0.26, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, the sample data does not show significant evidence that the mean number of friends for the student population at the college who use the social media website is larger than 150.
c)
1.The test statistic value is the difference between the sample mean and the null hypothesis value.
Which of the following is NOT a requirement of the Combinationsâ Rule, Subscript n Baseline Upper C Subscript requalsStartFraction n exclamation mark Over r exclamation mark (n minus r )exclamation mark EndFraction â, for items that are allâ different?
a. That r of the n items are selectedâ (without replacement).
b. That there be n different items available.
c. That order is not taken into accountâ (consider rearrangements of the same items to be theâ same).
d. That order is taken into accountâ (consider rearrangements of the same items to be differentâ sequences).
Answer:
d. That order is taken into account (consider rearrangements of the same items to be different sequences).
Step-by-step explanation:
Given the combination rule:
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
A major difference between permutation and combination is the order of the items in the selection. If the order does not matter then we have a combination. If on the other hand, the order of the items matter, then it is a permutation.
Therefore, that which is not a rule for combination is Option D since, in combination, we do not consider rearrangements of the same items to be different sequences.
what value of x makes the equation true ? 9.68x + 21.6 -6.23x = 2.3x + 17
Answer:
-4 please brainliest me
Step-by-step explanation:
9.68x+21.6-6.23x=2.3x+17
lets move it to the left
9.68x+21.6-6.23x-(2.3x+17)=0
Then, We add all the numbers together, and all the variables
3.45x-(2.3x+17)+21.6=0
We get rid of parentheses
3.45x-2.3x-17+21.6=0
We add all the numbers together, and all the variables
1.15x+4.6=0
We move all terms containing x to the left, all other terms to the right
1.15x=-4.6
x=-4.6/1.15
x=-4
x= -8 makes the equation true.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
9.68x + 21.6 -6.23x = 2.3x + 17
Now, solving for x
9.68 x - 6.23x - 2.3x = 17 - 21.6
1.15x= -4.6
x= -4.6 / 1.15
x= -8
Hence, x= -8 makes the equation true.
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