Answer:
The total weight of his purchase is 1.08 pounds
Step-by-step explanation:
To find the total weight of his purchase, we sum the weight of each of his purchases.
He purchased:
4/9 pound of peanut.
7/11 pounds of raisins
Total:
The least common multiple between 9 and 11 is 99.
Then
[tex]\frac{4}{9} + \frac{7}{11} = \frac{11*4 + 9*7}{99} = \frac{107}{99} = 1.08[/tex]
The total weight of his purchase is 1.08 pounds
A taxi company manager is trying to decide whether the use of radial tires instead of regular belted tires improves fuel economy. Twelve cars were equipped with radial tires and driven over a prescribed test course. Without changing drivers, the same cars were then equipped with regular belted tires and driven once again over the test course. The gasoline consumption, in kilometers per liter, was recorded as follows:
Car Radial-Tires Belted-Tires
1 4.2 4.1
2 4.7 4.9
3 6.6 6.2
4 7.0 6.9
5 6.7 6.8
6 4.5 4.4
7 5.7 5.7
8 6.0 5.8
9 7.4 6.9
10 4.9 4.7
11 6.1 6.0
12 5.2 4.9
A two-sample t-test was used to compare the mean kilometers per liter for the two types of tires using a .05 level of significance. The resulting p-value was .0152.
State the null and alternate hypotheses, state whether the null hypothesis should be rejected or not rejected and your reason for that conclusion, state the meaning of that conclusion specifically in terms of the problem being studied.
Answer:
Step-by-step explanation:
Corresponding gasoline consumption when radial tires is used and gasoline consumption when regular belted tires is used form matched pairs.
The data for the test are the differences between the gasoline consumption when radial tires is used and gasoline consumption when regular belted tires is used.
μd = the gasoline consumption when radial tires is used minus the gasoline consumption when regular belted tires is used.
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
The resulting p-value was .0152.
Since alpha, 0.05 > than the p value, 0.0152, then we would reject the null hypothesis. Therefore, at 5% significance level, we can conclude that the gasoline consumption when regular belted tires is used is higher than the gasoline consumption when radial tires is used.
A tree casts an 8-foot shadow on the ground. The length from the tip of the shadow to the top of the tree is 17 feet. What is the height of the tree?
Answer:
Height of tree = 15 ft
Step-by-step explanation:
Given:
Length of shadow (Base) = 8 ft
Length from the tip to top of the tree (Hypotenues) = 17 ft
Find:
Height of tree = ?
Computation:
Using Pythagoras theorem:
[tex]Height\ of\ tree = \sqrt{Hypotenues^2 - base^2} \\\\Height\ of\ tree = \sqrt{17^2 - 8^2} \\\\Height\ of\ tree = \sqrt{289-64}\\\\Height\ of\ tree = \sqrt{225}\\\\ Height\ of\ tree =15[/tex]
Height of tree = 15 ft
Answer:
The answer is 15 feet from the ground to the top of the tree.
Step-by-step explanation:
I am divisible by 3.
I am an even number.
I am the missing number
in 48/x=8.
Who am I?
Answer:
You are 6
Step-by-step explanation:
8×6=48 and 6/3=2
6 is even and fits in all of these areas.
Hope this helps.
Mark brainliest if correct.
Triangle ABC has been dilated about point A by a scale factor of One-third.
Triangle A B C. Side A C has a length of 39, side A B is 30, side C B is 48. Triangle A prime B prime C prime.
What are the lengths, in units, of the three sides of Triangle A prime B prime C prime?
Answer:
10,16,13
Step-by-step explanation:
got that right
The lengths of the sides of the triangle after the dilation is 13 , 10 and 16 respectively
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
Given data ,
Let the triangle be represented as ABC
Now , the dilated triangle is represented as A'B'C'
The dilation scale factor is d = 1/3
The measure of side AC = 39
The measure of side AB = 30
The measure of side BC = 48
Now , after the dilation of 1/3 , we get
The measure of side A'C' = 39 ( 1/3 ) = 13
The measure of side A'B' = 30 ( 1/3 ) = 10
The measure of side B'C' = 48 ( 1/3 ) = 16
Hence , the dilation triangle is having lengths 13 , 10 and 16
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What is simplified form of the fifth square root of x times the fifth square root of x times the fifth square root of x times the fifth square root of x
Answer: This was a bit hard to understand, x times the 5th root of x
Step-by-step explanation:
When you multiply square roots of the same root and inside value, they essentially get rid of the square roots. So the first two terms boil down to just x. Then multiply x by the 5th root of x to get:
[tex]x\sqrt[5]{x}[/tex]
Answer:
[tex]x[/tex]
Step-by-step explanation:
Apply exponent rules.
[tex]\sqrt{x} =x^\frac{1}{2}\\\:a^b\times \:a^c=a^{b+c}[/tex]
[tex]\sqrt[5]{x} \times\sqrt[5]{x} \times\sqrt[5]{x} \times\sqrt[5]{x} \times\sqrt[5]{x}[/tex]
[tex]x^{\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}}[/tex]
[tex]x^1[/tex]
Antoinette needs to solve this system of equations by graphing. Which statements explain how she should graph the equations? Check all that apply.
Answer:
see below
Step-by-step explanation:
In my opinion, Antoinette should make use of a graphing calculator to find the solution. (second attachment)
__
Slope-intercept form can be useful for graphing, so it often works well to start with equations in that form. If that is Antoinette's strategy, she should rewrite the first equation to that form. The second equation is already in slope-intercept form.
In doing that rewrite, she will want to get the y-term on one side of the equal sign by itself. She can do that by subtracting 2x from the first equation:
-7y = -2x +56
As a final step in her rewrite, she would divide by -7 to get ...
y = 2/7x +56
This 2nd equation has a positive slope of 2/7. The slope of the second equation is similarly the x-coefficient, -2.5. Neither is 4 and they have different signs.
The appropriate answer choices are shown checked below.
Answer:
B and D
Step-by-step explanation:
I got it right m8. Good day
How many days are there in 12 weeks? Use the following information to convert this time to days. 1 week = 7 days
Answer:
84days
Step-by-step explanation:
1 week = 7days =>12 weeks = 12×7 = 84days
Answer:
84 days are in 12 weeks
Step-by-step explanation:
1 week = 7 days
4 weeks = 28 days
So 28 + 28 + 28 = 84 days
Carole's age is five times Joe's age. The sum of their ages is 18. How old are Carole and Joe?
Answer:
Carole is 15
Joe is 3
Step-by-step explanation:
Carole's age is 15
Joes age is 3
3*5=15
15+3=18
Answer:
Carole = 15 Yrs
Joe = 3 Yrs
Step-by-step explanation:
15/5 =3
15+3 =18
Sry for the short explanation. Hope this helps!
Help asap giving branlist!!
Answer: Thr amount spent to manufacture each radio.
Step-by-step explanation: I put two and two together...lol...plz brainlest.
Answer:
The amount spent to manufacture each radio.
Step-by-step explanation:
125 is the start up cost and each radio costs 5.25 to make.
Solve for n.
11(n – 1) + 35 = 3n
n = –6
n = –3
n = 3
n = 6
Answer:
[tex]n = - 3[/tex]
Second answer is correct
Step-by-step explanation:
[tex]11(n - 1) + 35 = 3n \\ 11n - 11 + 35 = 3n \\ 11n - 3n = 11 - 35 \\ 8n = - 24 \\ \frac{8n}{8} = \frac{ - 24}{8} \\ n = - 3[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
lucy buys 3 liters of apple juice. How many millilitres of apple juice does she buy?
*please help*
Answer:
3000 milliliters
Step-by-step explanation:
1liter contains 1000militers
3liters contain (3*1000)militers
Answer:
3000 millilitres
Step-by-step explanation:
since 1 litre = 1000 millimetres
3 litres will be equal to 1000 x 3 = 3000 ml
In a recent survey, 10 percent of the participants rated Pepsi as being "concerned with my health." PepsiCo's response included a new "Smart Spot" symbol on its products that meet certain nutrition criteria, to help consumers who seek more healthful eating options. Suppose a follow-up survey shows that 18 of 100 persons now rate Pepsi as being "concerned with my health". Calculate the z statistic. (Round your answer to 2 decimal places.) zcalc At α = .05, would a follow-up survey showing that 18 of 100 persons now rate Pepsi as being "concerned with my health" provide sufficient evidence that the percentage has increased? Yes No
Answer: What what my you explain shorter please
Step-by-step explanation:
what are the answers to the following quadratic equation:
x^2-4x-12
Answer:
6 and -2
Step-by-step explanation:
x^2-4x-12
set up equal to zero
x^2-4x-12=0
lets factor:
(x-6)(x+2)=0
x-6=0
x=6
or
x+2=0
x=-2
Answer:
x=6 x=-2
Step-by-step explanation:
x^2-4x-12 = 0
Factor
What two numbers multiply to -12 and add to -4
-6*2 = -12
-6+2 = -4
(x-6)(x+2) =0
Using the zero product property
(x-6) =0 x+2 = 0
x=6 x=-2
The average score Josie had in 6 subjects is 72 and her average score after 2 additional subjects were added is 74.25. If she scored 80 in the 7th subject, what was her score in the 8th subject correct to the nearest whole number?
Answer:82
Step-by-step explanation:
a+b+c+d+e+f/6=72
a+b+c+d+e+f=6*72
a+b+c+d+e+f=432
a+b+c+d+e+f+g+h/8=74.25
a+b+c+d+e+f+g+h=594
g=80
h=?
432+80+h=594
512+h=594
h=82
hope it helps brainleast plz...
A random sample of 1,000 StatCrunchU students contains 598 female and 402 males. We analyze responses to the question, "What is the total amount (in dollars) of your student loans to date?" Two sample T confidence interval: μ 1: Mean of Loans where Gender="Female" μ 2: Mean of Loans where Gender="Male" μ 1 − μ 2: Difference between two means (without pooled variances) 95% confidence interval results: Difference Sample Diff. Std. Err. DF L. Limit U. Limit μ 1 − μ 2 516.74334 368.41116 907.34739 -206.29374 1239.7804 What can we conclude from the 95% confidence interval? Check all that apply. Group of answer choices
Based on the information given, these are the conclusions we can draw from the 95% confidence interval.
Here, we have,
From the provided 95% confidence interval, we can make the following conclusions:
The point estimate of the difference between the mean student loans for females and males is 516.74334 dollars.
The standard error of the difference between the means is 368.41116 dollars.
The degrees of freedom (DF) associated with the confidence interval is 907.34739.
The lower limit of the confidence interval is -206.29374 dollars.
The upper limit of the confidence interval is 1239.7804 dollars.
The confidence interval does not contain zero.
Since zero is not within the interval, we can conclude that the difference between the mean student loans for females and males is statistically significant at the 95% confidence level.
Based on the information given, these are the conclusions we can draw from the 95% confidence interval.
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The estimated difference in the mean student loans between females and males is 516.74334.
There is a 95% confidence that the true difference in means falls within the range of -206.29374 to 1239.7804.
Based on the 95% confidence interval provided for the difference in means between the loans of female and male StatCrunchU students, we can draw the following conclusions:
The sample difference in means is 516.74334.
The standard error of the difference is 368.41116.
The degrees of freedom (DF) for the analysis is 907.34739.
The lower limit of the confidence interval is -206.29374.
The upper limit of the confidence interval is 1239.7804.
Therefore, we can conclude the following:
The estimated difference in the mean student loans between females and males is 516.74334.
There is a 95% confidence that the true difference in means falls within the range of -206.29374 to 1239.7804.
Note: Since the confidence interval includes both positive and negative values, we cannot conclude with certainty whether there is a significant difference or not in the mean student loans between females and males. The confidence interval suggests that the difference could be positive, negative, or even zero.
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Solve for x. e^x - e ^ -x / e^x + e ^-x = t
Answer:
D
Step-by-step explanation:
(eˣ − e⁻ˣ) / (eˣ + e⁻ˣ) = t
Multiply by eˣ/eˣ.
(e²ˣ − 1) / (e²ˣ + 1) = t
Solve for e²ˣ.
e²ˣ − 1 = (e²ˣ + 1) t
e²ˣ − 1 = e²ˣ t + t
e²ˣ = 1 + e²ˣ t + t
e²ˣ − e²ˣ t = 1 + t
e²ˣ (1 − t) = 1 + t
e²ˣ = (1 + t) / (1 − t)
Solve for x.
2x = ln[(1 + t) / (1 − t)]
x = ½ ln[(1 + t) / (1 − t)]
Use log rule.
x = ln(√[(1 + t) / (1 − t)])
1960 were polled. 279 of them preferred Rock and Roll. What is the % of these students?
Answer:
14.2% students
Step-by-step explanation:
279 / 1960 = 0.142
0.142 x 100% = 14.2 %
Divide £2.28 btw eve and amelie in the ratio 9:5 give your answer to the nearest penny Eve gets ? And amelie gets ?
Answer:
Eve gets 1.47 and Amelie gets 0.81
Step-by-step explanation:
the ratio is 9 to 5 so we can say 9x + 5x=2.28
14x=2.28
x=0.16
so eve gets 9x = 9(2.28/14) = 1.47
and amelie gets 5x = 5(2.28/14) = 0.81
If a random sample of size 774 is selected, what is the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 3%
Suppose 43% of the population has a retirement account. If a random sample of size 774 is selected, what is the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 3%?
Answer:
the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 3% is 0.9082
Step-by-step explanation:
Given that:
sample size n = 774
Let P be the population proportion for having a retirement account = 0.43
Also
Let consider [tex]\hat p[/tex] be the sample proportion of having a retirement account.
However; as n is > 30 ; we can say:
[tex]\mathbf{\mu_{\hat p} = 0.43}[/tex] ;
[tex]\mathbf{\sigma_{\hat p^2} = \dfrac{p(1-p)}{n}}[/tex]
⇒ [tex]\mathbf{\sigma_{\hat p^2} = \dfrac{0.43(1-0.43)}{774}}[/tex]
⇒ [tex]\mathbf{\sigma_{\hat p^2} = \dfrac{0.43(0.57)}{774}}[/tex]
So; we need P( the sample proportion will differ from 'p' by less than 3% i.e 0.03)
[tex]=P(| \hat p- p|< 0.03)[/tex]
[tex]=P(| \hat p- \mu _p|< 0.03)[/tex]
[tex]= P ( |\dfrac{\hat P - \mu_p}{\sigma_{\hat p}}|< \dfrac{0.03}{\sqrt{ \dfrac{0.43*0.57}{774} }})[/tex]
[tex]= P(|Z|<1.6859)\ \ \ \ [Z=(\dfrac{\hat P - \mu_{\hat P}}{\sigma_{\hat P}}) \sim N(0,1)][/tex]
[tex]= P(-1.6859 <Z<1.6859) \\ \\ = \Phi(1.6859)- \Phi (-1.6859) \\ \\ = \Phi (1.6859) - (1- \Phi(1.6859) \\ \\ = 2 \Phi (1.6859)-1[/tex]
From Normal Cumulative Distribution Function Table
[tex]= 2*0.9541 -1[/tex]
= 1.9082 - 1
= 0.9082
Thus; the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 3% is 0.9082
A box is a cuboid with dimensions 28cm by 15cm by 20cm all measured to the nearest centimetre.
Disc cases are cuboid which measure 1.5 by 14.2 cm by 19.3 cm all measure to the nearest millimetre. Show that 17 disc cases, stacked as shown, will definitely fit the box
Answer:
The 17 disc cases would definitely fit into the box.
Step-by-step explanation:
The given cuboid box has the dimensions 28cm by 15cm by 20cm.
Disc cases are cuboid with dimensions 1.5cm by 14.2cm by 19.3cm.
volume of a cuboid = length × width × height
Volume of the box = 28 × 15 × 20
= 8400 cubic centimeters
Volume of each disc case = 1.5 × 14.2 × 19.3
= 411.09 cubic centimeters
When the 17 disc cases are stacked it would have a volume.
The volume of 17 disc cases = 17 × volume of a case
= 17 × 411.09
= 6988.53 cubic centimeters
Thus comparing the volume for 17 disc cases and that of the cuboid box, the disc cases would definitely fit into the box.
i.e = [tex]\frac{volume of box}{volume of 17 disc cases}[/tex]
= [tex]\frac{8400}{6988.53}[/tex]
= 1.20
Answer:
Step-by-step explanation:
27.5×14.5×19.5 =7775.625 cm³
1.55 x 14.25 x 19.35=427.393125
427.393125 x 17=7265.683
7775.625>7265.683
19.5x27.5x14.5=7775.625
1.45x14.15x19.25=394.961875
394.961875x17=6714.35
7775.63>6714.35
1.55x17=26.35
27.5>26.35
Explain how to find the range of a data set. Choose the correct answer below. A. The range is found by subtracting the first data entry from the last data entry. B. The range is found by adding the first and last data entries. C. The range is found by subtracting the minimum data entry from the maximum data entry. D. The range is found by adding the minimum and maximum data entries.
Answer:
C
Step-by-step explanation:
The range of a data set is the difference between the biggest and smallest values, so to find it, you just subtract the minimum from the maximum.
find the slope of the line through points 8,2 and -1,-4
Answer:
2/3
Step-by-step explanation:
We can find the slope by using the slope formula
m= (y2-y1)/(x2-x1)
= (-4-2)/(-1-8)
= -6/ -9
= 2/3
Translate the phrase into a variable expression. Use the letter d to name the variable. If necessary use the asterisk for multiplication and the slash for division The numbers of dollars Paul owes plus 16..
Answer:
This can be written as d + 16 because plus means addition.
A survey asks teachers and students whether they would like the new school
mascot to be a shark or a moose. This table shows the results. Which
statement is true?
Find the area of the smaller sector.
Round to the nearest tenth.
Help needed fast
Answer:
About 22.2 square feet
Step-by-step explanation:
First, you need to find the area of the full circle. The area of a circle is \pi r^2, which in this case is:
[tex]\pi r^2 = \pi \cdot 7.13^2\approx 159.628[/tex]
Now, since the sector is only 50 out of the total 360 degrees in a circle, you need to multiply this value by 50/360, which yields and area of about 22.2 square feet. Hope this helps!
A store has 80 modems in its inventory, 30 coming from Source A and the remainder from Source B. Of the modems from Source A, 20% are defective. Of the modems from Source B, 8% are defective. Calculate the probability that exactly two out of a sample of five modems selected without replacement from the store’s inventory are defective.
Answer:
0.102
Step-by-step explanation:
The number of defective modems in the inventory is 20% * 30 + 8% * 0.50 =10 (out of 80)
Note that the number of defectives in the inventory is fixed i.e. we are told that there is 1/8 probability that a modem in the inventory is defective, but rather that exactly 1/8 of all modems are defective.
The probability that exactly two modems in a random sample of five are defective is :
(10↓2)(70↓3) / (80↓5) = 0.102
A 2-pack of scented candles costs $0.95. What is the unit price, rounded to the nearest cent?i mark the 1st answer brainliest
Step-by-step explanation:
Cost of 2 pack = 0.95
Cost of 1 pack = 0.95 ÷ 2 = 0.475
Unit price = 0.475
simplify 2(f^4)^2/8f^12
Answer:
Step-by-step explanation:
2(f^4)^2/8(f^12)
2/8= 1/4
f^16/f^12
f^(16-12)= f^4
f^4/4 is the solution
A spherical gemstone just fits inside a plastic cube with edges 12cm. a) calculate the volume of gemstone, to the nearest cubic centimeter. b) how much empty space is there.
Answer:
a) (V) = 904.78 of a sphere = 288pi diameter = 12
(V) = 1728cm^3 of a cube = face diagonal = 16.9cm
b) Difference Volume = 1728-904.78 = 823.22cm^3
Step-by-step explanation:
To find volume of an inscribed sphere within a square cube
We use 4 π/3 * r^3 for the equation
As Radius = 6 = 6cm this is the only thing plugged into the equation to create a division first then a multiplication square of radius and then a multiplication. 4pi /3 * 6^3
r^3 = 216
4pi/3 = 4.18
4.18 * 216 = 904.78
This means the answer is 288 pi cm^3.
Answer:
volume of gemstone = 905 cm^3
volume of empty space = 823 cm^3
Step-by-step explanation:
volume of cube = s^3, where s = length of edge
volume of sphere = (4/3)(pi)r^3, where r = radius of sphere
The cube has a 12-cm edge. The sphere fits tightly inside the cube, so the diameter, d, of the sphere is 12 cm. The radius is half the diameter, so radius = r = diameter/2 = 12 cm/2 = 6 cm.
a)
volume of sphere = (4/3)(pi)r^3
volume of sphere = (4/3)(3.14159)(6 cm)^3
volume of sphere = 905 cm^3
b)
The empty space is the difference between the volume of the cube and the volume of the sphere.
volume of cube = s^3
volume of cube = (12 cm)^3
volume of cube = 1728 cm^3
empty space = volume of cube - volume of sphere
empty space = 1728 cm^3 - 905 cm^3
empty space = 823 cm^3
simplify 8-(3a+8)=
havent done these in a while so...
Answer:
3
Step-by-step explanation:
8-(3a+8)
8-(11a)
8-11a
a=11-8
a=3
Answer:
0
Step-by-step explanation:
8-(3a+8)=0
8-3a-8=0
-3a=0
a=0
