Both of you are correct because using either way can solve the equation for the value of x.
How to solve for x ?In the case of solving for x in 2/5 x = 14, the goal is to get rid of the fraction that is multiplying x on the left side. This can be done by either multiplying both sides of the equation by the inverse of 2 / 5 ( which is 5 / 2 ) or by dividing both sides by 2 / 5.
Doing either of these things would get rid of the 2 / 5 and give an answer to x as shown below :
Multiplying :
2/5 x = 14
5 / 2 x 2 / 5 x = 14 x 5 / 2
x = 35
Dividing :
2/5 x = 14
2 / 5 x / 2 / 5 = 14 / 2 / 5
x = 35
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Solid fats are more likely to raise blood cholesterol levels than liquid fats. Suppose a nutritionist analyzed the percentage of saturated fat for a sample of 6 brands of stick margarine (solid fat) and for a sample of 6 brands of liquid margarine and obtained the following results: Exam Image Exam Image We want to determine if there a significant difference in the average amount of saturated fat in solid and liquid fats. What is the test statistic
Answer:
[tex]t = 31.29[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{ccccccc}{Stick} & {25.8} & {26.9} & {26.2} & {25.3} & {26.7}& {26.1} \ \\ {Liquid} & {16.9} & {17.4} & {16.8} & {16.2} & {17.3}& {16.8} \ \end{array}[/tex]
Required
Determine the test statistic
Let the dataset of stick be A and Liquid be B.
We start by calculating the mean of each dataset;
[tex]\bar x =\frac{\sum x}{n}[/tex]
n, in both datasets in 6
For A
[tex]\bar x_A =\frac{25.8+26.9+26.2+25.3+26.7+26.1}{6}[/tex]
[tex]\bar x_A =\frac{157}{6}[/tex]
[tex]\bar x_A =26.17[/tex]
For B
[tex]\bar x_B =\frac{16.9+17.4+16.8+16.2+17.3+16.8}{6}[/tex]
[tex]\bar x_B =\frac{101.4}{6}[/tex]
[tex]\bar x_B =16.9[/tex]
Next, calculate the sample standard deviation
This is calculated using:
[tex]s = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]
For A
[tex]s_A = \sqrt{\frac{\sum(x - \bar x_A)^2}{n-1}}[/tex]
[tex]s_A = \sqrt{\frac{(25.8-26.17)^2+(26.9-26.17)^2+(26.2-26.17)^2+(25.3-26.17)^2+(26.7-26.17)^2+(26.1-26.17)^2}{6-1}}[/tex]
[tex]s_A = \sqrt{\frac{1.7134}{5}}[/tex]
[tex]s_A = \sqrt{0.34268}[/tex]
[tex]s_A = 0.5854[/tex]
For B
[tex]s_B = \sqrt{\frac{\sum(x - \bar x_B)^2}{n-1}}[/tex]
[tex]s_B = \sqrt{\frac{(16.9 - 16.9)^2+(17.4- 16.9)^2+(16.8- 16.9)^2+(16.2- 16.9)^2+(17.3- 16.9)^2+(16.8- 16.9)^2}{6-1}}[/tex]
[tex]s_B = \sqrt{\frac{0.92}{5}}[/tex]
[tex]s_B = \sqrt{0.184}[/tex]
[tex]s_B = 0.4290[/tex]
Calculate the pooled variance
[tex]S_p^2 = \frac{(n_A - 1)*s_A^2 + (n_B - 1)*s_B^2}{(n_A+n_B-2)}[/tex]
[tex]S_p^2 = \frac{(6 - 1)*0.5854^2 + (6 - 1)*0.4290^2}{(6+6-2)}[/tex]
[tex]S_p^2 = \frac{2.6336708}{10}[/tex]
[tex]S_p^2 = 0.2634[/tex]
Lastly, calculate the test statistic using:
[tex]t = \frac{(\bar x_A - \bar x_B) - (\mu_A - \mu_B)}{\sqrt{S_p^2/n_A +S_p^2/n_B}}[/tex]
We set
[tex]\mu_A = \mu_B[/tex]
So, we have:
[tex]t = \frac{(\bar x_A - \bar x_B) - (\mu_A - \mu_A)}{\sqrt{S_p^2/n_A +S_p^2/n_B}}[/tex]
[tex]t = \frac{(\bar x_A - \bar x_B) }{\sqrt{S_p^2/n_A +S_p^2/n_B}}[/tex]
The equation becomes
[tex]t = \frac{(26.17 - 16.9) }{\sqrt{0.2634/6 +0.2634/6}}[/tex]
[tex]t = \frac{9.27}{\sqrt{0.0878}}[/tex]
[tex]t = \frac{9.27}{0.2963}[/tex]
[tex]t = 31.29[/tex]
The test statistic is 31.29
A random sample of individuals at an airport were asked, "Is your flight on time or delayed?" Below are the results of the survey in a joint relative frequency table.
On time Delayed Total
Domestic 96 412
International 76
Total 147
Part A: Draw and complete the frequency table. (3 points)
Part B: What is the smallest joint frequency, and what does it represent in the context? (3 points)
Part C: Does the data show an association between the flight being on time and flying domestic? If so, is it positive or
negative? (4 points)
Answer:
A.
domestic: 316 / 96 / 412
international: 76 / 51 / 127
total: 392 / 147 / 539
B. 51 its the smallest number
C. I don't know what association means but 76.2% of domestic flights land on time and 63% of international flights land on time so id say its positive
A company is producing picture frames as well as the glass for the front of the frames. The amount of wood required
for the frame is represented by the function W/(x), and the amount of glass is represented by the function G(x). The
frames have lengths represented by the function f(x) and widths represented by g(x).
X
2
3
4
5
W(x)=2[(f+g)(x)]
14
24
34
44
G(x) = (f-g)(x)
6
27
60
105
Which statement describes the combined functions W(x) and G(x)?
O The amount of glass required has a constant rate of change, but the amount of wood does not.
O The amount of wood required has a constant rate of change, but the amount of glass does not.
O Both the amount of wood required and the amount of glass required have a constant rate of change.
ONeither the amount of wood required nor the amount of glass required has a constant rate of change.
Answer:The combined functions W(x) and G(x) represent the amount of wood and glass required to produce a picture frame. Based on the information provided,
W(x)= 2[(f+g)(x)] and G(x) = (f-g)(x)
By looking at the values of the given table, it can be observed that the rate of change in the amount of glass required (G(x)) is not constant, it increases as x increases.
On the other hand, the rate of change in the amount of wood required (W(x)) is not constant as well, it increases as x increases too.
It's not mentioned any information about constant rate of change for f and g.
Therefore, the correct statement that describes the combined functions W(x) and G(x) is: "Neither the amount of wood required nor the amount of glass required has a constant rate of change."
It's important to mention that the problem provided does not have a unique solution, because the values for f and g are not defined so it's not possible to infer their behaviour over time.
It is only possible to infer the behaviour of the functions W(x) and G(x) given the information provided, and it is clear that the rate of change for both functions does not remain constant, but it increases as x increases.
Step-by-step explanation:
Help please ????????????
Answer:
700 i think-
Step-by-step explanation:
Jahnay is following this recipe to make cakes. Jahnay uses 780 g of butter. How many cakes is Jahnay making? Recipe: Makes 1 Cake 120 g sugar 130 g butter 260 g flour 3 eggs
Jahnay is making 6.5 cakes from the given ingredients.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
Recipe: Makes 1 Cake = 120 g sugar + 130 g butter + 260 g flour + 3 eggs.
Jahnay is following this recipe to make cakes.
Jahnay uses 780 g of butter.
To find the number of cakes:
Use division operation,
780 ÷ 120,
= 780/120
= 78/12
= 6.5
Therefore, Jahnay makes 6.5 cakes.
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A box contains 3 plain pencils and 9 pens. A second box contains 9 color pencils and I crayon. One item from each box is chosen at random. What is the
probability that a pen from the first box and a crayon from the second box are selected?
Write your answer as a fraction in simplest form.
Pls help i only have 2 minuets left
Answer:
14, 3!
Step-by-step explanation:
It is very complicated to explain.
I need help right away!!
Answer:
i think its c though im not sure
Step-by-step explanation:
Find the volume of the cone. Round your answer to the nearest hundredth
Answer:
[tex]V=8042.47\ cm^3[/tex]
Step-by-step explanation:
Given that,
The radius of the cone, r = 16 cm
The height of the cone, h = 30 cm
The slant height of the cone, l = 34 cm
We need to find the volume of the cone. The formula for the volume of a cone is given by :
[tex]V=\dfrac{1}{3}\pi r^2 h[/tex]
Put all the values,
[tex]V=\dfrac{1}{3}\times \pi \times (16)^2 \times 30\\\\V=8042.47\ cm^3[/tex]
So, the volume of the cone is equal to [tex]8042.47\ cm^3[/tex].
Suppose you have fewer than 10 place value blocks. How many different ways could you show 1214? Explain.
There are 3,024 different ways 1,214 can be shown.
What is permutation?Basically A permutation is an arrangement of items in a specific direction or sequence. One should consider both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important. The permutation is seen as an ordered combination, in other words.
Given 1,214
since there are 4 places in the digit,
so 4 values less than 10 can be solved by
9, 8, 7, and 6
so by permutation to find ⁹P₄ = 9!/(9 - 4)!
= (9 x 8 x 7 x 6 x5!)/5!
⁹P₄ = 3,024
Hence there are 3,024 different ways.
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pls help, last question. the one circled in red
On solving the provided question, we can say that - in the linear equation y = 1/2x + 5, slope, m = 1/2
What is a linear equation?The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
here,
in the linear equation =>
y = +1/2x + 5
on comparing with y = mx +c
slope, m = 1/2
and, c= +5
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please HELPPPPP according to the Marcus trail mix recipe 2 cups of dry food should be used for every 3 1/2 cups of salted nuts at this rate how many cups of nuts should be used for 3 cups are dried fruit is used?
Determine whether Rolle's Theorem applies to the following function on the given interval. If so, find the point(s) that are guaranteed to exist by Rolle's Theorem.
g(x) = x3 + x2-x-1:(-1,1)
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. Rolle's Theorem applies and the point(s) guaranteed to exist is/are x =
(Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)
B. Rolle's Theorem does not apply.
Answer:
I have attached the answers
when a positive integer was multiplied by each of its digits, the product was 1995. Find the original number.
Answer:
57
Step-by-step explanation:
You want a positive number that gives a product of 1995 when it is multiplied by each of its digits.
NumberThe prime factors of 1995 are 3, 5, 7, 19. The product of 3 and 19 gives 57, so multiplying 57 by 5 and 7 will result in the product 1995.
The original number is 57.
<95141404393>
Please help me guys also i would like the answer to be type out instead of a pic of it alot more easier for me thanks
Answer:I think it’s 10718.571428571 but rounded to a tenth it’s 10724.6
Step-by-step explanation: 10,150+10211+10424+10769+10844+11155+11477 divided by 7 equals 10718.571428571 or 10724.6.
What is the equation of the least squares regression line for the data set?
The equation of the least squares regression line for the data set is (b) ŷ = -2.984x + 112.38
How to determine the equation of the least squares regression line for the data setFrom the question, we have the following parameters that can be used in our computation:
Volunteer 15 11 22 35 18 41 27 18
Trees 77 99 4 11 44 14 2 90
Using a graphing calculator, we have the following calculation summary
Sum of X = 187Sum of Y = 341Mean X = 23.375Mean Y = 42.625Sum of squares (SSX) = 741.875Sum of products (SP) = -2213.875The regression equation is represented as
ŷ = bX + a
Where
b = SP/SSX = -2213.88/741.88 = -2.98416
a = MY - bMX = 42.63 - (-2.98*23.38) = 112.37978
So, we have
ŷ = -2.98416X + 112.37978
Approximate
ŷ = -2.984x + 112.38
Hence, the equation is ŷ = -2.984x + 112.38
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Find the compound ratio of 2:3 and 5:4
The compound ratio of natural number ratios 2 : 3 and 5 : 4 is equal to 5 : 6.
How to determine a compound ratio
Herein we must determine a compound ratio, that is, the product of two ratios, whose definition is shown below:
For a : b and c : d, where a, b, c, d are natural numbers, the compound ratio is equal to (a · c) / (b · d).
If we know that a : b = 2 : 3 and c : d = 5 : 4, then the compound ratio is equal to:
r = (2 · 5) : (3 · 4)
r = 10 : 12
Finally, we simplify the resulting expression:
r = 5 : 6
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which fractions, when converted, result in a repeating decimal? select all that apply 1/8 1/6 3/12 8/9 2 and 4/5 4 and 3/11
Answer:
B. 1/6
D. 3/12
F. 4 3/11
PLEASE MARK BRAINLIEST
New repost of my question
Answer:
Step-by-step explanation:
???
Work out the cost of 12kg of potatoes and 1 1/2kg of carrots
Answer:
The cost is #15.90
Step-by-step explanation:
See comment for complete question
Given
[tex]P \to Potato[/tex]
[tex]C \to Carrot[/tex]
[tex]3P + 2C = 5.08[/tex]
[tex]P = 1.24[/tex]
Required
[tex]12P + 1\frac{1}{2}C = ??[/tex]
First, we solve for C
Substitute [tex]P = 1.24[/tex] in [tex]3P + 2C = 5.08[/tex]
[tex]3 * 1.24 + 2C = 5.08[/tex]
[tex]3.72 + 2C = 5.08[/tex]
Collect like terms
[tex]2C = 5.08 - 3.72[/tex]
[tex]2C = 1.36[/tex]
Solve for C
[tex]C = \frac{1.36}{2}[/tex]
[tex]C = 0.68[/tex]
So, we have:
[tex]P = 1.24[/tex]
[tex]C = 0.68[/tex]
[tex]12P + 1\frac{1}{2}C = ??[/tex] becomes
[tex]12P + 1\frac{1}{2}C = 12*1.24 + 1\frac{1}{2}*0.68[/tex]
[tex]12P + 1\frac{1}{2}C = 14.88 + 1.02[/tex]
[tex]12P + 1\frac{1}{2}C = 15.90[/tex]
what line
no association
nonlinear association
positive linear association
negative linear association
I believe that is a negative linear association.
Ricky went to sleep at 9:45 pm and woke up at 6:30 the next morning. For how long did he sleep?
Answer:
8 hours and 45 minutes.
Step-by-step explanation:
Write in standard form 0.0003251
Answer:
Step-by-step explanation:
The answer is 3.2510 x 10^-4
A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 27 weeks. Assume that the length of unemployment is normally distributed with population mean of 27 weeks and the population standard deviation of 2 weeks. Suppose you would like to select a random sample of 39 unemployed individuals for a follow-up study.
Required:
a. What is the distribution of X?
b. What is the distribution of xÌ?
c. What is the probability that d. For 36 unemployed individuals, find the probability that the average time that they found the next job is less than one randomly selected individual found a job less than 27 weeks?
Answer:
X ~ N(27, 4) ;
xbar ~ N(27, 0.1026) ;
0.5 ;
0.5
Step-by-step explanation:
Probability distribution of X : N(μ, σ²)
μ = 27 ; σ = 2
X ~ N(μ, σ²) = X ~ N(27, 2²) ;X ~ N(27, 4)
Distribution is approximately normal ; μ = xbar ; xbar = 27
(Standard Error)² = (σ/√n)²= (2/√39)² = 0.1026
xbar ~ N(μ, σ²) = xbar ~ N(27, 2²) ; xbar ~ N(27, 0.1026)
Probability that a randomly selected individual found a job in less than 27 weeks :
P(X < 27) :
Obtain the Zscore :
Z = (x - μ) / σ
Z = (27 - 27) / 2 = 0/2
Z = 0
P(Z < 0) = 0.5
D.) n = 36
P(X < 27) :
Obtain the Zscore :
Z = (x - μ) / σ/√n
Z = (27 - 27) / (2/√36) = 0/0.33333
Z = 0
P(Z < 0) = 0.5
Write an equation of a line that is perpendicular to 6x - 3y = -6 and passes
through the point (-12, 14).
I'm sorry but I didn't get that
please explain step by step in full process
questions
Given L || M find the value of unknown angles in each of the following figures
Answer:
x = 120°
y = 60°
Step-by-step explanation:
✔️since, lines l and m, area parallel, therefore,
x = 120° (they are corresponding angles having matching corners. Thus, corresponding angles are congruent to each other)
✔️x + y = 180° (linear pair angles)
Plug in the value of x
120 + y = 180
Subtract 120 from each side of the equation
y = 180 - 120
y = 60°
Can someone please help asap
Answer:
the answer is 38
Step-by-step explanation:
because one of the angles is 90 and the other one is 45, so the other angle is 45 too
so.. this is an isosceles triangle
A _____ is a flat surface that has no thickness.
Select each equation that the number 10^3 makes true.
6.01 x
= 601
O 0.305 x
= 305
0.54 x
= 540
O 0.097 x
970
0.97 x
= 97
All of the equations which the number 10³ makes true include the following:
B. 0.305 × __ = 305
C. 0.54 × __ = 540
How to determine the true equations?In this exercise, you are required to determine the equations which the number 10³ makes true. This ultimately implies that, we would substitute the number 10³ into each of the given equations as follows;
6.01 × 10³ = 601
By expanding the exponent, we have the following equation:
6.01 × 1,000 = 601
6010 = 601 (False).
0.305 × 10³ = 305
By expanding the exponent, we have the following equation:
0.305 × 1,000 = 305
305 = 305 (True).
0.54 × 10³ = 540
By expanding the exponent, we have the following equation:
0.54 × 1,000 = 540
540 = 540 (True).
0.097 × 10³ = 970
By expanding the exponent, we have the following equation:
0.097 × 1,000 = 970
97 = 970 (False).
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Miguel rode his bike to work which was 15 miles from home. However he was too tired to ride back so he got a ride in a
car from a co-worker. He spent a total of 2 hours traveling. The average speed of traveling by car was 3 times faster
than on his bike. What was Miguel's average speed on his bike and in the car?
Answer:
Bike: 10 miles per hour
Car: 30 miles per hour
Step-by-step explanation:
He spent: 2h/(1+3) = 0,5h by car and 0,5h x 3 = 1,5h by bike
The car is: 15 miles/ 0,5h = 30 miles/h
The bike is: 15 miles/ 1,5h = 10 miles/h