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Zepler [3.9K]
3 years ago
11

What is the value of w? 28=4(w−3)

Mathematics
2 answers:
sveticcg [70]3 years ago
7 0

Answer:

w=10

Step-by-step explanation:

1. Divide 4 on both sides to cancel out the 4 on the right side since it is an equation so it has to remain “equal”/ balanced.

2. You get 7=w-3.

3. Add 3 on both sides.

4.You get w=10.

Ostrovityanka [42]3 years ago
6 0

Answer:

w=10

Step-by-step explanation:

-DIvide both sides by 4

28/4=w-3

-Simplify 28/4

7=w-3

-Add 3 to both sides

7+3=w

-Simplify 7+3 to 10

10=w

-Flip it

w=10

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Consider the accompanying data on breaking load (kg/25mm width) for various fabrics in both an unabraded condition and an abrade
WITCHER [35]

Answer:

The critical value for a one-tailed test with 7 degrees of freedom and level of significance α=0.01 is tc=2.998.

The test statistic (t=1.729) is below the critical value and falls within the acceptance region, so it is failed to reject the null hypothesis.

At a significance level of 0.01, there is not enough evidence to support the claim that the true difference is significantly bigger than 0.

Step-by-step explanation:

We have a matched-pair t-test for the difference.

We have the null and alternative hypothesis written as:

H_0: \mu_d=0\\\\H_a: \mu_d>0

We have n=8 pairs of data. We calculate the difference as:

d_1=U_1-A_1=36.4-28.5=7.9

Then, with this procedure we get the sample for d:

d=[7.9,\, 35,\, 5.5,\, 4.2,\, 6.7,\, -3.7,\, -0.9,\, 3.3]

The sample mean and standard deviation are:

M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{8}(7.9+35+5.5+. . .+3.3)\\\\\\M=\dfrac{58}{8}\\\\\\M=7.25\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{7}((7.9-7.25)^2+(35-7.25)^2+(5.5-7.25)^2+. . . +(3.3-7.25)^2)}\\\\\\s=\sqrt{\dfrac{985.08}{7}}\\\\\\s=\sqrt{140.73}=11.86\\\\\\

Now, we can perform the one-tailed hypothesis test.

The significance level is 0.01.

The sample has a size n=8.

The sample mean is M=7.25.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=11.86.

The estimated standard error of the mean is computed using the formula:

s_M=\dfrac{s}{\sqrt{n}}=\dfrac{11.86}{\sqrt{8}}=4.1931

Then, we can calculate the t-statistic as:

t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{7.25-0}{4.1931}=\dfrac{7.25}{4.1931}=1.729

The degrees of freedom for this sample size are:

df=n-1=8-1=7

This test is a right-tailed test, with 7 degrees of freedom and t=1.729, so the P-value for this test is calculated as (using a t-table):

\text{P-value}=P(t>1.729)=0.0637

As the P-value (0.0637) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.01, there is not enough evidence to support the claim that the true difference is significantly bigger than 0.

If we use the critical value approach, the critical value for a one-tailed test with 7 degrees of freedom and level of significance α=0.01 is tc=2.998. The test statistic is below the critical value and falls within the acceptance region, so it is failed to reject the null hypothesis.

8 0
3 years ago
What is 36 pieces of candy for 6 children as a unit rate?
Leni [432]

\frac{36}{6} =\frac{6}{1}

7 0
3 years ago
Consider randomly selecting a student at a large university. Let A be the event that the selected student has a Visa card, let B
Tems11 [23]

Answer:

0.75

Step-by-step explanation:

Given,

P(A) = 0.6, P(B) = 0.4, P(C) = 0.2,

P(A ∩ B) = 0.3, P(A ∩ C) = 0.12, P(B ∩ C) = 0.1 and P(A ∩ B ∩ C) = 0.07,

Where,

A = event that the selected student has a Visa card,  

B = event that the selected student has a MasterCard,  

C = event that the selected student has an American Express card,

We know that,

P(A ∪ B ∪ C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C)

= 0.6 + 0.4 + 0.2 - 0.3 - 0.12 - 0.1 + 0.07

= 0.75

Hence, the probability that the selected student has at least one of the three types of cards is 0.75.

5 0
2 years ago
Nicole plans to watch 3 movies each month . Write an equation to represent the total number of movies n that she will watch in m
kramer
N=3x, x is months and n is the total.
3 0
3 years ago
Solve by substitution <br> X^2= 2y + 10<br> 3x-y = 9
Viefleur [7K]

Answer:

x=-4\\ x=-2\\ y=-21\\ y=-15

Step-by-step explanation:

x^{2} =2y+10

y=-9+3x

x^{2} =2(-9+3x)+10

x^{2} =-18+6x+10

x^{2} =6x-8

x^{2} -6x+8

x=-4, -2

y=-9+3(-4)

y=-9-12

y=-21

y=-9+3(-2)

y=-9-6

y=-15

8 0
3 years ago
Read 2 more answers
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