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2 years ago

Peter bought 90 boards for $270.

1 answer:

8 0

The algebraic expression would be
n=$270/90
the value of n to the expression is equal to 3 meaning that 20 boards would cost $60

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helpppppppppppppppp need now--------------------------------------------------Manuel borrowed $1,500 from his bank and signed a

Sedaia [141]

Answer: I think it’s 225
Explanation: 1,500 • .15= 225

3 0

3 years ago

D=a+b+c solve for b<br> I need some help

Hoochie [10]

Hi Walker

d=a+b+c

Flip

a+b+c=d

Add -a to both sides

a+b+c-a=d-a

b+c=-a+d

Now add -c to both sides

b+c-c=-a+d-c

b= -a-c+d

I hope that's help:0

4 0

2 years ago

Sarah claims that the thickness of the spearmint gum she produces is 7.5 one-hundredths of an inch. A quality control specialist

satela [25.4K]

Answer:

$t=\frac{7.55-7.5}{\frac{0.103}{\sqrt{10}}}=1.539$

$p_v =2*P(t_{(9)}>1.539)=0.158$

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis.

Step-by-step explanation:

Data given and notation

Data: 7.65, 7.60, 7.65, 7.7, 7.55, 7.55, 7.4, 7.4, 7.5, 7.5

We can begin calculating the sample mean given by:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And the sample deviation given by:

$s=\sart{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And we got:

$\bar X=7.55$ represent the sample mean

$s=0.103$ represent the sample standard deviation

$n=10$ sample size

$\mu_o =7.5$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is equal to 7.5 or no, the system of hypothesis would be:

Null hypothesis: $\mu = 7.5$

Alternative hypothesis: $\mu \neq 7.5$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{7.55-7.5}{\frac{0.103}{\sqrt{10}}}=1.539$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=10-1=9$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(9)}>1.539)=0.158$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis.

3 0

3 years ago

Y is 1 less than 2 times X which order pair fits this rule

Anni [7]

Answer:

y < 2X - 1

y = 2X - 1

Step-by-step explanation:

Let's try to make an equation from the worded problem.

"is Less than " means <

2 times means 2 * X

= 2X

y < 2X - 1

y = 2X - 1

3 0

3 years ago

Determine whether parallelogram JKLM with vertices J(-7, -2), K(0, 4), L(9, 2) and M(2, -4) is a rhombus, square, rectangle or a

White raven [17]

Check the picture below

now, we know is a parallelogram, so the diagonals will bisect

looking at the picture, the interior angles are not right-angles, and thus is not a rectangle, and is not a square either, due to the same reason

is it a rhombus? well, a rhombus, is a parallelogram, that's "slanted" per se, but regardless of how slanted it may be, the sides are all equal

now, we don't need to check the length of both pairs, just one of the segments of each pair, let's check only then JK and KL, the ones in red in the picture, since each pair of segments are twin, if JK = KL, then that means all sides are equal

$\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
J&({{-7 }}\quad ,&{{ -2}})\quad 
% (c,d)
K&({{ 0}}\quad ,&{{ 4}})\\\\
K&({{ 0}}\quad ,&{{ 4}})\quad 
% (c,d)
L&({{ 9}}\quad ,&{{ 2}})
\end{array}\qquad 
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
JK=\sqrt{[0-(-7)]^2+[4-(-2)]^2}\implies JK=\sqrt{(0+7)^2+(4+2)^2}
\\\\\\
JK=\sqrt{7^2+6^2}
\\\\\\
KL=\sqrt{(9-0)^2+(2-4)^2}\implies KL=\sqrt{9^2+(-2)^2}$

now... another characteristic of a rhombus is, the diagonals, meet at right-angle, that means KM ⟂ JL

and that simply means, if you get the slope of KM and the slope of JL, the product of their slope is -1

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
K&({{ 0}}\quad ,&{{ 4}})\quad 
% (c,d)
M&({{ 2}}\quad ,&{{ -4}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-4-4}{2-0}$

$\bf -------------------------------\\\\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
J&({{ -7}}\quad ,&{{ -2}})\quad 
% (c,d)
L&({{ 9}}\quad ,&{{ 2}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{2-(-2)}{9-(-7)}\implies \cfrac{2+2}{9+7}$

then multiply both slopes, if their product is -1, that means, they're perpendicular to each other, and it IS a rhombus only, then.

7 0

3 years ago

Read 2 more answers