Answer:
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Which means that the first number is 104, the second number is 104 + 1 and the third number is 104 + 2. Therefore, three consecutive integers that add up to 315 are 104, 105, and 106.
Step-by-step explanation:
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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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
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:
What is the average rate of change for this function for the interval from x= 1
to x = 3?
Answer:
The average rate of change is 12x=12.0x.
Description:
Function: x= 1x = 3 convert to short form: x 1x 3
Interval: x= 1 , x 3
Steps:
Input: Find the average rate of change of f(x)=3x2 on the interval [x,3x].
We have that a=x, b=3x, f(x)=3x2
Thus, f(b)−f(a)b−a=3((3x))2−(3(x)2)3x−(x)=12x.
Answer: the average rate of change is 12x=12.0x.
Please mark brainliest
Hope this helps.
Answer:
3
Step-by-step explanation:
A P E X
Which decimal is closest in value to 9/20
Answer:
0.45
Step-by-step explanation:
9/20 is the same as 0.45
Answer:
0.45
Step-by-step explanation:
9/20= 9*5/20*5= 45/100= 0.45
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!!!
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.
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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.
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.
If a man takes 30 minutes to drive at work and it is 44 miles into work what is the average speed?
Answer:
1.46666 miles / minutes
88 miles per hour
Step-by-step explanation:
The speed is distance over time
44 miles / 30 minutes
1.46666 miles / minutes
or if we want in miles per hour
44 miles / .5 hours
88 miles per hour
Answer:
1.467 mile/minute
Step-by-step explanation:
you should divide the distance on the time i.e. 44/30
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]
build the greatest and the smallest number using the digit 7,2,6
greatest _____ and smallest ____
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) Use the power series expansions for ex, sin x, cos x, and geometric series to find the first three nonzero terms in the power series expansion of the given function.
(b) Based on the information given in the section on algebraic properties of power series, for which values of x can you guarantee that the new series converges.
(If you have a CAS, you can easily find several more nonzero terms in the power series expansions of the functions.)
(e^x)/(cos(x))
Answer:
a) [tex]\mathbf{4 + \dfrac{x}{1!}- \dfrac{2x^2}{2!} ...}[/tex]
b) See Below for proper explanation
Step-by-step explanation:
a) The objective here is to Use the power series expansions for ex, sin x, cos x, and geometric series to find the first three nonzero terms in the power series expansion of the given function.
The function is [tex]e^x + 3 \ cos \ x[/tex]
The expansion is of [tex]e^x[/tex] is [tex]e^x = 1 + \dfrac{x}{1!}+ \dfrac{x^2}{2!}+ \dfrac{x^3}{3!} + ...[/tex]
The expansion of cos x is [tex]cos \ x = 1 - \dfrac{x^2}{2!}+ \dfrac{x^4}{4!}- \dfrac{x^6}{6!}+ ...[/tex]
Therefore; [tex]e^x + 3 \ cos \ x = 1 + \dfrac{x}{1!}+ \dfrac{x^2}{2!}+ \dfrac{x^3}{3!} + ... 3[1 - \dfrac{x^2}{2!}+ \dfrac{x^4}{4!}- \dfrac{x^6}{6!}+ ...][/tex]
[tex]e^x + 3 \ cos \ x = 4 + \dfrac{x}{1!}- \dfrac{2x^2}{2!} + \dfrac{x^3}{3!}+ ...[/tex]
Thus, the first three terms of the above series are:
[tex]\mathbf{4 + \dfrac{x}{1!}- \dfrac{2x^2}{2!} ...}[/tex]
b)
The series for [tex]e^x + 3 \ cos \ x[/tex] is [tex]\sum \limits^{\infty}_{x=0} \dfrac{x^x}{n!} + 3 \sum \limits^{\infty}_{x=0} ( -1 )^x \dfrac{x^{2x}}{(2n)!}[/tex]
let consider the series; [tex]\sum \limits^{\infty}_{x=0} \dfrac{x^x}{n!}[/tex]
[tex]|\frac{a_x+1}{a_x}| = | \frac{x^{n+1}}{(n+1)!} * \frac{n!}{x^x}| = |\frac{x}{(n+1)}| \to 0 \ as \ n \to \infty[/tex]
Thus it converges for all value of x
Let also consider the series [tex]\sum \limits^{\infty}_{x=0}(-1)^x\dfrac{x^{2n}}{(2n)!}[/tex]
It also converges for all values of x
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:
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
Fractions - Addition : 3/7 + 1/56
Explanation needed
[tex]answer = \frac{25}{56} \\ solution \\ \frac{3}{7} + \frac{1}{56} \\ = \frac{3 \times 8 + 1}{56} \\ = \frac{24 + 1}{56} \\ = \frac{25}{56} \\ hope \: it \: helps \: \\ good \: luck \: on \: your \: assignment[/tex]
Answer:
25/56
Step-by-step explanation:
3/7 + 1/56
We have to find the L.C.M of 7 and 56
The L.C.M of 7 and 56 is 56
Now, we have to change the denominators to 56
we dont need to change the denominator of 1/56 to 56 as it is already 56
[tex]\frac{3}{7}[/tex] * [tex]\frac{8}{8}[/tex] = [tex]\frac{24}{56}[/tex]
Now we can add the fractions
[tex]\frac{24}{56} + \frac{1}{56}[/tex] [tex]= \frac{25}{56}[/tex]
Hope it helped :>
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)
Sarah wants to refurbish her shop.
She is quoted £2500 for the refurbishment, with a 20% discount to be taken off.
What is the final cost of the refurbishment after the discount?
Answer:
2000
Step-by-step explanation:
2500 / 100 = 25 (1%)
25 X 20 =500 (20%)
2500 - 500 =2000
An online shopping website collected data regarding its operations and obtained the following linear regression model for the estimated revenue in millions, Y-hat, based on the click-through rate in thousands, x. Y-hat = 1.2+0.2x
What is the best interpretation of the value of the estimated slope of 0.2?
Answer:
There is an estimated increase in revenue of $0.2 million for each 1,000 additional clicks
Step-by-step explanation:
The slope (0.2) is the rate of change in Y-hat for each unit change in x.
In this specific case, since Y-hat is the revenue, in millions, and x is the number of clicks, in thousands, the best interpretation is that there is an estimated increase in revenue of $0.2 million for each 1,000 additional clicks
How can you use mathematics to help scientists explore Martian Craters ?
Answer:
Mathematics could make scientists to have a preliminary understanding of the dimensions, perimeters, areas and volumes of different craters on Mars.
Step-by-step explanation:
Martian Craters are series of craters formed on the surface of Mars. The study of a planets crater gives an understanding of the properties of matter that lies under the crater.
Mathematics can be applied to determine the dimensions, perimeter, area and volume of the features of a crater using appropriate conversions and theorems.
The Pi in the sky theorem can be applied to determine the area and perimeter, even volume of different craters on the Mars surface. Also, eingenfunction expansion theorem gives a preliminary knowledge of the craters.
By measurements and conversions processes, the features of Martian crater could be studied from images.
The length of a rectangle is increasing at a rate of 8 cmys and its width is increasing at a rate of 3 cmys. When the length is 20 cm and the width is 10 cm, how fast is the area of the rectangle increasing?
Answer:
The area of the rectangle increasing at the rate of 140 cm²/s
Step-by-step explanation:
Rectangle area:
A rectangle has two dimensions, length l and width w.
It's area is:
A = l*w.
When the length is 20 cm and the width is 10 cm, how fast is the area of the rectangle increasing?
We apply implicit differentiation to solve this question:
[tex]A = l*w[/tex]
So
[tex]\frac{dA}{dt} = l\frac{dw}{dt} + w\frac{dl}{dt}[/tex]
Length is 20, so [tex]l = 20[/tex].
Width is 10, so [tex]w = 10[/tex]
The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 3 cm/s.
This means that [tex]\frac{dl}{dt} = 8, \frac{dw}{dt} = 3[/tex]
So
[tex]\frac{dA}{dt} = l\frac{dw}{dt} + w\frac{dl}{dt}[/tex]
[tex]\frac{dA}{dt} = 20*3 + 10*8 = 140[/tex]
Area in cm².
So
The area of the rectangle increasing at the rate of 140 cm²/s
6q+4-q+5 please right now
Answer:
5q + 9
Step-by-step explanation:
Combine like terms to simplify the expression.
Have a blessed day!
Answer:
7q+9
Step-by-step explanation:
6q+4+q+5
6q+q+4+5
=7q+9
1.
On hand: Magnesium sulfate 30 grams is mixed in 500 ml Lactated Ringers. Order: infuse a
maintenance dose of magnesium sulfate at 4 grams/hour. At what rate should the nurse set the
pump:
Answer:
The IV will run [tex]66.67 \ ml /hr[/tex]
Step-by-step explanation:
From the question we are told that
The mass of Magnesium sulfate is [tex]m_g = 30 \ g[/tex]
The volume of the Magnesium sulfate [tex]V_R = 500ml[/tex]
The rate at which the dose of the solution (Magnesium sulfate + Lactated Ringers. ) is infused is [tex]R = 4g/hr[/tex]
The concentration of Magnesium sulfate in Lactated Ringers is mathematically evaluated as
[tex]C_m = \frac{m_g}{V_R}[/tex]
substituting values
[tex]C_m = \frac{30}{500}[/tex]
[tex]C_m = 0.06\ g/ ml[/tex]
This implies that
0.06 g of Magnesium sulfate is in every 1 ml of Lactated Ringers
So 4 g of Magnesium sulfate is in x ml of Lactated Ringers
So
[tex]x = \frac{4}{0.06}[/tex]
[tex]x = 66.67 \ ml[/tex]
So the amount of the solution in ml that is been infused in 1 hour is
[tex]66.67 \ ml /hr[/tex]
What is the additive inverse of the complex number 9-4i?
Answer:
[tex] \frac{1}{9 - 4i} [/tex]
I'm not sure
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.
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
HELP PLEASE
Answer:
y=2/3x+1
Step-by-step explanation:
The slope is 2/3 and the y-intercept is 1.
Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
15 m
12 m
0
9 m
11 m
Thanks for anyone that answers
Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write all numbers as integers or simplified fractions.
7x + 6y + 4z = 10
3x + 3y + 3z - 1
4x + 4y + 4z = 2
Part: 0/2
Part 1 of 2
Evaluate the determinants D, Dx Dy and Dz.
D=
Dx=
Dy=
Dz=
Answer:
D = 0 , Dx = 4 , Dy = -6 , Dz = 2
Step-by-step explanation:
As per cramer's rule,
D = | 7 6 4 | = 0
| 3 3 3 |
| 4 4 4 |
Dx = | 10 6 4 | = 4
| 1 3 3 |
| 2 4 4 |
Dy = | 7 10 4 | = -6
| 3 1 3 |
| 4 2 4 |
Dz = | 7 6 10 | = 2
| 3 3 1 |
| 4 4 2 |
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!
