The length of the hypotenuse of a right triangle is 16 inches. If the length of one leg is 5 inches, what is the approximate length of the other leg? 10.5 inches 11.0 inches 15.2 inches 16.8 inches

Answer:

[tex]x> \frac{8}{51} [/tex]

Step-by-step explanation:

[tex]7x - \frac{5}{8} x + 3>4[/tex]

Bring constants to one side, simplify:

[tex] \frac{51}{8} x>4 - 3 \\ \frac{51}{8} x>1 \\ x>1 \div \frac{51}{8} \\ x>1 \times \frac{8}{51} \\ x> \frac{8}{51} [/tex]

*Note that the inequality sign only changes when you divide the whole inequality by a negative number.

Answer:

[tex]x>\frac{8}{51}[/tex]

Step-by-step explanation:

[tex]7x-\frac{5}{8}x+3>4\\\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}\\7x-\frac{5}{8}x+3-3>4-3\\\mathrm{Simplify}\\7x-\frac{5}{8}x>1\\\mathrm{Multiply\:both\:sides\:by\:}8\\7x\times \:8-\frac{5}{8}x\times \:8>1\times \:8\\\mathrm{Simplify}\\56x-5x>8\\51x>8\\\mathrm{Divide\:both\:sides\:by\:}51\\\frac{51x}{51}>\frac{8}{51}\\\\x>\frac{8}{51}[/tex]

I hope it helps :)

Answer:36

Step-by-step explanation:

Answer:

each ice coffee is $2.25

Step-by-step explanation:

13.50 - 9 = 4.50

4.50 / 2 = 2.25

Answer:

[tex]m = -j[/tex], or in this case, [tex]m=-(-7)[/tex]

Step-by-step explanation:

Assuming that Justine's score is represented by [tex]j[/tex] and Meagan's score is represented by [tex]m[/tex], we know that [tex]j[/tex] will always be the opposite of [tex]m[/tex].

To represent opposite, we put a negative sign before the variable.

This makes the current number, even if it's negative, the opposite value.

Let's test it out.

Since Justine's score is -7, substituting it into the equation makes it  [tex]m=-(-7)[/tex]. We know that two negatives make a positive, so [tex]m=7[/tex].

Now let's assume Justine's score is 7. Plugging it into the equation, we get [tex]m=-(7)[/tex]. That's the same thing as [tex]m = -1(7)[/tex], and -1 times 7 is -7.

Hope this helped!

Answer:

d. 31% of the variance in characters per word is accounted for by words per sentence.

Step-by-step explanation:

The coefficient of determination is the statistical measurement that determines the impact in difference of one variable which is explained by the difference in another variable. It is denoted by [tex]R^{2}[/tex] or R-squared. It helps in predicting the outcome of the event.

Answer:

4 units

Step-by-step explanation:

A transformation is the movement of a point from one position to another position. If a shape is transformed all its points are also transformed. Types of transformations are translation, rotation, reflection and dilation.

If a shape is transformed, the length of its sides and shape remains the same, only the position changes.

If Line segment AB has a length of 4 units. It is translated 1 unit to the right on a coordinate plane to obtain line segment A'B, the length of A'B' remains the same which is 4 unit. To prove this:

Let A be at ([tex]x_1,y_1[/tex]) and B be at ([tex]x_2,y_2[/tex]). The length of AB is:

[tex]AB=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

If AB is translated to the right by 1 unit the new points are A' at ([tex]x_1+1,y_1[/tex]) and B' at ([tex]x_2+1,y_2[/tex]). The length of A'B' is:

[tex]A'B'=\sqrt{(y_2-y_1)^2+(x_2+1-(x_1+1))^2}=\sqrt{(y_2-y_1)^2+(x_2+1-x_1-1)^2}\\\\A'B'=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

AB = A'B' = 4 units

Answer:

The probability that the diagnosis is correct is 0.95249.

Step-by-step explanation:

We are given that the American Diabetes Association estimates that 8.3% of people in the United States have diabetes.

Suppose that a medical lab has developed a simple diagnostic test for diabetes that is 98% accurate for people who have the disease and 95% accurate for people who do not have it.

Let the probability that people in the United States have diabetes = P(D) = 0.083.

So, the probability that people in the United States do not have diabetes = P(D') = 1 - P(D) = 1 - 0.083 = 0.917

Also, let A = event that the diagnostic test is accurate

So, the probability that a simple diagnostic test for diabetes is accurate for people who have the disease = P(A/D) = 0.98

And the probability that a simple diagnostic test for diabetes is accurate for people who do not have the disease = P(A/D') = 0.95

Now, the probability that the diagnosis is correct is given by;

    Probability = P(D) [tex]\times[/tex] P(A/D) + P(D') [tex]\times[/tex] P(A/D')

                      = (0.083 [tex]\times[/tex] 0.98) + (0.917 [tex]\times[/tex]0.95)

                      = 0.08134 + 0.87115

                      = 0.95249

Hence, the probability that the diagnosis is correct is 0.95249.

Answer:

18 outfits

Step-by-step explanation:

To determine the number of outfits available

3 shirts * 3 pairs of pants * 2 pairs of shoes

3*3*2

18

Answer:

B

Step-by-step explanation:

The weight of the jar depends on the number of marbles in it, therefore the weight is the dependent variable (y) and the number of marbles is the independent variable (x). The y-intercept is when x = 0 and since the number of marbles is x, the answer is that the y-intercept represents the weight of the jar without the marbles.

Answer:

[tex]A.\ 16\sqrt3\ cm^2[/tex] is the correct answer.

Step-by-step explanation:

Given that:

Side of an equilateral triangle = 8 cm

To find:

Area of the triangle will be:

[tex]A.\ 16\sqrt3\ cm^2[/tex]

[tex]B.\ \dfrac{32}{3} cm^2[/tex]

[tex]C.\ 48\ cm^2[/tex]

[tex]D.\ 36\sqrt3\ cm^2[/tex]

Solution:

First of all, let us have a look at the formula for area of an equilateral triangle:

[tex]A =\dfrac{\sqrt3}{4}a^2[/tex]

Where [tex]a[/tex] is the side of equilateral triangle and an equilateral triangle is a closed 3 sided structure in 2 dimensions which has all 3 sides equal to each other.

Here, we are given that side, [tex]a=8\ cm[/tex]

Putting the value in formula:

[tex]A =\dfrac{\sqrt3}{4}\times 8^2\\\Rightarrow A =\dfrac{\sqrt3}{4}\times 64\\\Rightarrow A =\sqrt3\times 16\\OR\\\Rightarrow \bold{A =16\sqrt3\ cm^2}[/tex]

Hence, [tex]A.\ 16\sqrt3\ cm^2[/tex] is the correct answer.

Answer:

6 sandwiches to choose from because

3×2 = 6

Answer:

(0,9.8) and (10, 1.2)

Step-by-step explanation:

These are the only points that are the best fit for the garph correlation.

Answer:

(0, 9.8) and (10, 1.2)

Step-by-step explanation:

:) hope this helped

Answer:

800700

Step-by-step explanation:

800000 + 00000 + 0000 + 000 + 00 + 0

000000 + 00000 + 0000 + 700 + 00 + 0

------------------------------------------------------------

= 800700

Answer:

Hey there!

800000+700=800700

Hope this helps :)

Answer:

13

Step-by-step explanation:

A)5+5=10

B)5+7=12

C) impossible

D)7+7=14

E)5+5+5=15

Nope, i dont think so

Answer:

no the numbers are infinite

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The term 3x² has 2 as an exponent, the correct option is C.

Exponents are the base raised by power, it is written in the superscript of a number.

The expression is  3x² +y-5

The term 3x² has 2 as an exponent.

Therefore, the correct option is C.

The missing options are

A.3x2

B. y

A 2

C. -5

D. None of these choices are correct.

To know more about Exponents

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Answer:

I know the answer

Step-by-step explanation:

Courtney made 60% of her shots

Answer:

she made a 60%

Step-by-step explanation:

first you do this 3÷5

that gives you .60

inorder to get a percent multiply by 100

that gives you an end result of 60

add the percent sing and your done 60%

hope i helped

Answer:

B.y = –2.9x + 13.5 i think dont word me for it

Step-by-step explanation:

Equation of line is y = –2.9x + 13.5 which is correct option(B).

A linear equation is defined as an equation in which the highest power of the variable is always one.

Let y = a + bx, where a is the y-intercept and b is the slope.

[tex]\sum{x} = 1 + 2 + 3 + 4 + 5 = 15[/tex]

[tex]\sum{y} = 11 + 8 + 4+ 1 + 0 = 24[/tex]

[tex]\sum {xy} = 11 + 16 + 12 + 4 + 0 = 43[/tex]

[tex]\sum{x^2} = 1 + 4 + 9 + 16 + 25 = 55[/tex]

[tex]n = 5[/tex]

[tex]b= \dfrac{n\sum{xy}-\sum{x}\sum{y}}{n{\sum{x^2}-(\sum{x}})^2}[/tex]

[tex]b= \dfrac{ 5 (43) - (15) . (24)}{{5 (55) - (15})^2}[/tex]

[tex]b= -2.9[/tex]

[tex]a = \dfrac{25}{5} - (-2.9)\dfrac{15}{5}[/tex]

[tex]a=13.5[/tex]

Hence, equation of line is y = –2.9x + 13.5

Learn more about linear equation here:

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Answer:

the answer will be 2 to 12

Answer:

2 to 12

Step-by-step explanation:

just did a quiz got it right

Answer: Vu is 15 years old now.

Step-by-step explanation:

Let present age of WU be x.

Then, the present age of Vu = 3x

Also, After 25 years

Age of Wu = x+25

According to the question:

[tex](x+25)=2(3x)\\\\\Rightarrow\ x+25=6x\\\\\Rightarrow\5x=25\\\\\Rightarrow\ x=5[/tex]

Present age of Vu = 3(5) = 15

Hence, Vu is 15 years old now.

Answer:

j

Step-by-step explanation:j

Answer:

Option A.

Step-by-step explanation:

The given equation of ellipse is

[tex]4x^2+9y^2=36[/tex]

Divide both sides by 36.

[tex]\dfrac{4x^2}{36}+\dfrac{9y^2}{36}=1[/tex]

[tex]\dfrac{x^2}{9}+\dfrac{y^2}{4}=1[/tex]

[tex]\dfrac{x^2}{3^2}+\dfrac{y^2}{2^2}=1[/tex]    ...(1)

The standard form of an ellipse is

[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]    ...(2)

where, (h,k) is center, (h±a,k) are vertices and (h±c,k) are foci.

On comparing (1) and (2), we get

[tex]h=0,k=0,a=3,b=2[/tex]

Now,

Center [tex]=(h,k)=(0,0)[/tex]

Vertices [tex]=(h\pm a,k)=(0\pm 3,0)=(3,0),(-3,0)[/tex]  

We know that

[tex]c=\sqrt{a^2-b^2}=\sqrt{3^2-2^2}=\sqrt{5}[/tex]

Foci [tex]=(h\pm c,k)=(0\pm \sqrt{5},0)=(\sqrt{5},0),(-\sqrt{5},0)[/tex]

Therefore, the correct option is A.

Answer:

The least possible price is  p  =  £110

Step-by-step explanation:

From the question we are told that

     The number of bracelets to be made is  [tex]n = 150[/tex]

      The length of silver require for on bracelet is  [tex]x = 26 \ cm = 0.26 \ m[/tex]

      The option of silver length packs that she buys is  a =  10.5 m  packs

                                                                                           b  =  3.7 m packs

    Generally

                   1 bracelet   [tex]\to[/tex]  0.26 m  

                   150 bracelet [tex]\to[/tex]  z

=>        [tex]z = \frac{150 * 0.26}{1}[/tex]

=>        [tex]z = 39 \ m[/tex]

Now for option a  i.e  10.5 m  per pack

    The number of packs require is

        [tex]v = \frac{z}{a}[/tex]

=>     [tex]v = \frac{39}{ 10.5}[/tex]

=>      [tex]v = 3.7 1[/tex]

given that the number of packs cannot be a fraction but an integer hence she needs to purchase v =  4

and that 4 packs would equal  t  =  4 * 10.5 =  42 meters of  silver

 Now for option d  i.e  3.7 meters per pack  

 The number of packs requires is  

           [tex]w = \frac{z}{b}[/tex]

=>        [tex]w = \frac{39}{3.7}[/tex]

=>        [tex]w = 10.54[/tex]

given that the number of packs cannot be a fraction but an integer hence she needs to purchase w= 11

and that 11 packs would equal  t  = 11 * 3.7 =  40.7 meters of  silver

So the comparing the option and option b we see that for her to pay as little as possible she needs to go for option b since option be will produce the 150  bracelet with a little excess while option a will produce the 150 bracelet with much excess

    Assuming the price for the 3.7 m  pack is    £10

     And the price for the 10.7 pack is  £30

The least possible amount she would pay is  

                 [tex]p = 10 * 11[/tex]

                 p  =  £110  

Answer:

B

Step-by-step explanation:

Calculate the ratio of corresponding sides, image to preimage, that is

scale factor = [tex]\frac{DE}{AC}[/tex] = [tex]\frac{12.09}{16.12}[/tex] = 0.75 → B

The scale factor of the dilation will be 1.33. Then the correct option is A.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

There is no effect of dilation on the angle.

In the diagram, ∆ABC and ∆DBE are similar.

Then the scale factor of the dilation that will map the preimage ΔABC onto the image ΔDBE will be

⇒ 16.12 / 12.09

⇒ 1.33

Then the correct option is A.

More about the dilation link is given below.

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Answer:

(-5, 0) and (0,4)

Step-by-step explanation:

Given equation: -4x + 5y = 20

Sub. in the values

When x = -5 and y = 0 (-5,0),

[tex] - 4( - 5) + 5(0) = 20 [/tex]

When x = 0 and y = 4 (0,4),

[tex] - 4(0) + 5(4) = 20[/tex]

That's how I would do it, not sure if your school has another method. Hope this helps :)

Answer: x = -5 and y = 4

Step-by-step explanation: its the first option do you need me to exlain how cuz its multiple choice  

Answer:

The sample size is  [tex]n = 2401[/tex]

Step-by-step explanation:

From the question we are told that

    The margin of  error is  [tex]E= 2\% = 0.02[/tex]

Given that the  confidence level is  95% then the level of significance is mathematically evaluated as

          [tex]\alpha = (100 - 95)\%[/tex]

            [tex]\alpha = 5\% = 0.05[/tex]

The  critical value of [tex]\frac{\alpha }{2}[/tex]  obtained from the normal distribution table is   [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]  

Let assume that the sample proportion is  [tex]\r p = 0.5[/tex]

 Generally the sample size is evaluated as

            [tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \r p ( 1- \r p )[/tex]

            [tex]n = [\frac{1.96}{0.02} ]^2 * 0.5 ( 1- 0.5 )[/tex]

            [tex]n = 2401[/tex]

Answer:

total number(n)=10

divided the total number into two equal parts so

in one group of number =5

ln first phase group of number middle value =44

In second phase group of number middle value=50

then using formula,q1=44 q3=50

inter quartile range =q3_q1

=50-44

=6

therefore interquartile range =6

Answer: The answer is 6

Answer:

x² + 7x + 49/4 = (x + 7/2)²

Step-by-step explanation:

x² + bx + c is a perfect square when c = (b/2)².

b = 7, c = (7/2)² = 49/4.

x² + 7x + 49/4 = (x + 7/2)²

Answer:

x² + 7x + 12.25 = (x+3.5)²

Step-by-step explanation:

(a+b)² = a²+ 2ab + b²

then:

7x = 2ab

7/2 = 3.5

then:

(x+3.5)² = x² + 2*3.5*a + 3.5²

x² + 7x + 12.25 = (x+3.5)²

Answer:

3* 10 ^12

Step-by-step explanation:

(5x10^7)(6x10^4)

Multiply the numbers together

5*6 =30

Add the exponents

10^7 * 10 ^ 4 = 10 ^(7+4) = 10 ^11

30 * 10 ^11

But this is not scientific notation since 30 >10

Move the decimal one place to the left and add 1 to the exponent

3* 10 ^12

Answer:

3* 10 ^12

Step-by-step explanation: