The diagonals of quadrilateral EFGH intersect at D(1,3). EFGH has vertices at E(2,6) and F(-4,5). What must be the coordinates of G and H to ensure that EFGH is
a parallelogram?

Answer:

6741

Step-by-step explanation:

if its 10% smaller you would have to do the original precent, which is 100%, and subtract 10%, (90%) then divide 90 by 100 to get 0.9 and  multiply it by the total population, in this case 7,490, and you get your answer. i hope this helps :)

Answer:

92.9

Step-by-step explanation:

8.90 times 6 equals 53.40

7.90 times 5 equals 39.50

39.50 plus 53.40 equals 92.9

The probability that out of 20, 14 agree to answer is:

P(14) = 0.109

We know that the 80% of the respondents will agree to answer the opinion poll (and 20% don't).

Then the probability that a random respondent agrees to answer the poll is 0.8

Now, the probability that out of 20, 14 agree to answer, is:

[tex]P(14) = C(20, 14)*(0.8)^{14}*(0.2)^6[/tex]

Where C(20, 14) is the number of different combinations of 14 elements that we can make out of the 20 elements (the number of permutations).

[tex]C(20, 14) = \frac{20!}{(20 - 14)!*14!} = \frac{20*19*18*17*16*15}{6*5*4*3*2} = 38,760[/tex]

Replacing that in the probability, we get:

[tex]P(14) = 38,760*(0.8)^{14}*(0.2)^6 = 0.109[/tex]

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Using the t-distribution, as we have the standard deviation for the sample, it is found that it can be concluded that the holes are being punched an average of 1. 84 cm.

At the null hypotheses, it is tested if the mean is of 1.84 cm, that is:

[tex]H_0: \mu = 1.84[/tex]

At the alternative hypothesis, it is tested if the mean is different of 1.84 cm, that is:

[tex]H_1: \mu \neq 1.84[/tex]

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

Considering the hypothesis and the given sample, it is found that the parameters are as follows:

[tex]\overline{x} = 1.85, \mu = 1.84, s = 0.0235, n = 12[/tex].

Hence, the test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{1.85 - 1.84}{\frac{0.0235}{\sqrt{12}}}[/tex]

[tex]t = 1.47[/tex]

Considering a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.1 and 12 - 1 = 11 df, the critical value is of [tex]|t^{\ast}| = 1.7959[/tex]

Since the absolute value of the test statistic is less than the critical value, we do not reject the null hypothesis and it can be concluded that the holes are being punched an average of 1. 84 cm.

More can be learned about the t-distribution at https://brainly.com/question/16313918

Step-by-step explanation:

2 ( 5 - 3 ) + 3 ( 3 )

2 × 2 + 9 = 4 + 9 = 13

Answer:

x = 3 , x = 7

Step-by-step explanation:

3(x - 5)² - 17 = - 5 ( add 17 to both sides )

3(x - 5)² = 12 ( divide both sides by 3 )

(x - 5)² = 4 ( take square root of both sides )

x - 5 = ± [tex]\sqrt{4}[/tex] = ± 2 ( add 5 to both sides )

x = 5 ± 2

then

x = 5 - 2 = 3

x = 5 + 2 = 7

1) The x-axis represents the energy ([tex]E[/tex]), in joules. The y-axis represents the amplitude ([tex]x[/tex]), in milimeters.

2) The curve depicts an monotonous decrecent rate of change.

3) The amplitude is directly proportional to the root square of the energy.

In this question we have a relationship between two variables, in which we must apply principles of functional analysis to respond three questions presented in the statement.

Now we proceed to answer the three questions below:

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Answer:

1 pair of jeans and 3 sweatshirts

Step-by-step explanation:

41-17=24

24/8=3

The inequality shows the number of sweatshirts Monique can buy along with one pair of jeans if she has $41 to spend  will be; 17x + 8y ≤ 41

An inequality is a mathematical statement that compares two values or expressions using a relational operator, such as less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), or not equal to (≠). Inequalities are used to describe relationships between quantities or to express constraints or conditions.

We are given that clothing store is selling a pair of jeans for $17 and a sweatshirt for $8.

Therefore,

41-17=24

Unit price = 24/8=3

Thus 1 pair of jeans and 3 sweatshirts

The inequality shows the number of sweatshirts Monique can buy along with one pair of jeans becomes as;

17x + 8y ≤ 41

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Answer:29.2

Step-by-step explanation:The equation used to add a markup percent to a product is the cost plus the markup percentage multiplied by the cost.

Answer:

$29.20

Step-by-step explanation:

The original price of an item is 100%, so a 60% mark up means that the price will now be 160% of the original price.

160% = 160/100 = 1.6

⇒ 160% of $18.25 = 1.6 × 18.25 = $29.20

Answer:

  49.2 square yards

Step-by-step explanation:

The surface area of a rectangular prism can be found using the formula.

  A = 2(LW +H(L +W)) . . . . where L, W, H are length, width, height

  A = 2(3×5 +1.2(3 +5)) = 2(15 +9.6) = 49.2 . . . . square yards

The length of the colony is the product of 5. 3 × 10^3 and the length of the bacteria

The total length of the colony is 143.1 mm

The given parameters are:

Bacteria = 2.7 × 10^–2 mm.

Colony = 5. 3 × 10^3 of the bacteria

So, the length (L) of the colony is:

[tex]L = 5.3 * 10^3 * 2.7 * 10^{-2[/tex]

Rewrite as:

[tex]L = 5.3 * 2.7* 10^3 * 10^{-2[/tex]

Evaluate the products

[tex]L = 14.31* 10[/tex]

Evaluate the product

[tex]L = 143.1[/tex]

Hence, the total length of the colony is 143.1 mm

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Answer:

For example, 16/21

Step-by-step explanation:

Are there choices?

There is an infinite number of numbers between any two numbers.

2/3 = 14/21

6/7 = 18/21

One example of a fraction between 2/3 and 6/7 is 16/21

16/21 is between 2/3 and 6/7.

Answer:

y = 0

x = 4

Explanation:

make x the subject,

x - 3y = 4

x = 4 + 3y __ equation 1

2x - 5y = 8

x = (8+5y)/2 __ equation 2

using substitution method:

(8+5y)/2 = 4 + 3y

8 + 5y = 8 + 6y

6y - 5y = 8 - 8

y = 0

Find x,

x = 4 + 3y

x = 4 + 3(0)

x = 4

Answer:

x = 4

y = 0

Step-by-step explanation:

x - 3y = 4      (original)

x = 4 + 3y     (rewritten)

2x -5y = 8                 (second equation)

2(4 + 3y) - 5y = 8      (substitute 4 + 3y for x)

2(4 + 3y) - 5y = 8        (distribute)

8 + 6y - 5y = 8            (combine like terms)

y = 0                           (first variable)

x - 3y = 4            (original)

x - 3(0) = 4          (substitute 0 for y)

x = 4                  (second variable)

You can double check this by plugging these numbers back into each equation; x = 4 and y = 0 is true for both.

I hope this helps!

Answer: [tex]4\frac{4}{5}[/tex]

Step-by-step explanation:

To see how many [tex]\frac{1}{6}[/tex] pound servings are in [tex]\frac{4}{5}[/tex] of a pound of chicken we must divide [tex]\frac{4}{5}[/tex] by [tex]\frac{1}{6}[/tex]

[tex]\frac{4}{5}[/tex]÷[tex]\frac{1}{6}[/tex]

When dividing by a fraction you can take the reciprocal (flip the numerator and denominator) and you can multiply instead of dividing

[tex]\frac{4}{5}[/tex]×[tex]\frac{6}{1}[/tex]=[tex]\frac{24}{5}[/tex]=[tex]4 \frac{4}{5}[/tex]

Answer:

24/5, or 4.8, servings

Step-by-step explanation:

Let s represent the number of servings. We have:

[tex] \frac{1}{6} s = \frac{4}{5} [/tex]

[tex]s = \frac{24}{5} = 4.8[/tex]

Answer:

2/15

Step-by-step explanation:

Given:

A box contains 4 white balls and 6 yellow balls. A ball is drawn at random from the box and is not replaced. What is the probability that both balls are white?

8/45

3/25

4/25

2/15

Solve:

Knowing that total = 10 { 4 white balls and 6 yellow balls}

P(first white)=4/10=2/5 { 4 out of 10 balls are white}

P(second white)=3/9=1/3 { 3 out of 9 balls are white; Since no replaced}

P(both white)=2/5 × 1/3=2/15

Hence, Answer = 2/15

Lenvy~

Answer 116•6 feet

Hope it is helpful

Step-by-step explanation:

(f-g)(x) = f(x) - g(x)

the same applies to all other basic operations (like addition, multiplication, ...).

so,

(f-g)(x) = 4x² - 3 - (x + 1) = 4x² - 3 - x - 1 = 4x² - x - 4

Answer:

try the option provided in the attachment.

Table B and C are represent the function.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

To find which relations below represent functions.

Now,

We know that;

A relation between a set of inputs having one output each is called a function.

Hence, By table 1;

Each output has same input.

Thus, Its not represent function.

By table 2;

A set of inputs having one output each.

Hence, Its represent function.

By table 3;

A set of inputs having one output each.

Hence, Its represent function.

Thus, Table B and C are represent the function.

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Answer:

$31.05

Step-by-step explanation:

You can get this answer by changing percent (13.5%) to just 13.5, or in other words, a decimal. you also change 230. to a decimal by by moving the decimal point two times to the left to get 2.30. You can then get your answer by multiplying the values together (2.30 x 13.5)

Answer:

A tangent to a circle is a straight line which touches the circle at only one point.  Therefore, if [tex]x=2y+5[/tex] is a tangent of [tex]x^2+y^2=5[/tex] then there will be one point of intersection.

To find the point of intersection, substitute [tex]x=2y+5[/tex] into [tex]x^2+y^2=5[/tex] and solve for y:

[tex]\implies (2y+5)^2+y^2=5[/tex]

[tex]\implies 4y^2+20y+25+y^2=5[/tex]

[tex]\implies 5y^2+20y+20=0[/tex]

[tex]\implies y^2+4y+4=0[/tex]

[tex]\implies (y+2)^2=0[/tex]

[tex]\implies y+2=0[/tex]

[tex]\implies y=-2[/tex]

Substitute found value of y into [tex]x=2y+5[/tex] and solve for x:

[tex]\implies x=2(-2)+5=1[/tex]

Therefore, there is one point of intersection at (1, -2), thus proving that the straight line equation is a tangent to the circle.

Hey there!

The first step in solving this equation is

2(7x-3)=9

14x-6=9

Now, add 6 to both sides:

14x=15

Divide both sides by 14:

x=15/14

Hope everything is clear.

Let me know if you have any questions!

#ILoveLearning:-)

Given:

[tex]\\[/tex]

❍Let's assume, Length of rectangle x feet and width of the rectangle x - 5 feet respectively.

[tex]\\[/tex]

To calculate the dimensions of the rectangle we will use the formula of Area of rectangle:

[tex]\\[/tex]

[tex] \: \: \: \: \: \: \: { \underline{ \boxed{ \pmb{ \frak{ Area_{(rectangle)} = Length \times width }}}}} \\ \\ [/tex]

[tex]\\[/tex]

[tex] \underline {\sf{Substituting \: the \: values~ in~ above~formula: }} \\ [/tex]

[tex]\\[/tex]

[tex] : \implies \sf \:x \times (x - 5) = 126 \\ \\ \\ : \implies \sf \:x^2 - 5x = 126 \\ \\ \\ : \implies \sf \:x^2 - 5x - 126 = 0 \\ \\ \\ : \implies \sf \:x^2 - 14x - 9x - 126 = 0 \\ \\ \\ : \implies \sf \:x (x - 14) - 9 (x + 14) = 0 \\ \\ \\ : \implies \sf \:(x - 14)(x - 9) = 0 \\ \\ \\ : \implies { \boxed { \purple{\pmb { \: x = 14 \: \: or \: \: x = -9}}} } \\ \\ \\ [/tex]

Hence,

[tex]\\[/tex]

[tex] \\ { \underline{ \pmb{ \frak{\therefore Dimensions \: of \: rectangle \: are \: 9~ feet \: and \: 14 ~feet \: }}}}[/tex]

Given that, width of the rectangle is 5 feet less than the length and area of the rectangle is 126 sq. feet, and we are told to find the dimensions i.e the length and width of the rectangle.

As we know that the area of a rectangle is length times it's width, so if we assume our length to be x, so our width is just going to be (x - 5) , and putting it in the area formule we can thus obtain;

[tex]{:\implies \quad \sf x(x-5)=126}[/tex]

[tex]{:\implies \quad \sf x^{2}-5x-126=0}[/tex]

[tex]{:\implies \quad \sf x^{2}-14x+9x-126=0}[/tex]

[tex]{:\implies \quad \sf x(x-14)+9(x-14)=0}[/tex]

[tex]{:\implies \quad \sf (x-14)(x+9)=0}[/tex]

So, here either (x - 14) = 0 or (x + 9) = 0, when you equate both, you will get x = 14 or -9 but as x ≠ -9, so x = 14, and then x - 5 = 14 - 5 = 9

Hence, the required length and width are 14 feet and 9 feet respectively

Answer:

[tex]y = \frac{1}{3} x^2[/tex]

Step-by-step explanation:

Vertical stretch = widens graph

Factor = multiply by [tex]\frac{1}{3}[/tex]

FINAL RESULT: [tex]y = \frac{1}{3} x^2[/tex]

Hope this helps!

Answer:

  x = -3/2

Step-by-step explanation:

To find the unknown value, substitute all known values and solve for the one remaining. After substitution, this becomes a 2-step linear equation, so is solved by the procedure for such equations.

  y = -6x +5 . . . . . given

  14 = -6x +5 . . . . substitute known value

  9 = -6x . . . . . . . subtract 5 (step 1)

  9/-6 = x = -3/2 . . . . divide by the coefficient of x (step 2);

Hello!

In order to find the value of x, we should take the value of y and plug it in and then simplify.

[tex]\bold{y=-6x+5}[/tex]

Plug in:

[tex]\bold{14=-6x+5}[/tex]

Switch places:

[tex]\bold{-6x+5=14}[/tex]

Now, subtract 5 from both sides:

[tex]\bold{-6x=14-5}[/tex]

[tex]\bold{-6x=9}[/tex]

Divide both sides by -6 in order to isolate x:

[tex]\bold{x=-\displaystyle\frac{9}{6}}[/tex]

Can this fraction be reduced? Sure, we can divide the numerator (9) and the denominator (6) by 3:

[tex]\bold{-\displaystyle\frac{3}{2}}[/tex]

As a Mixed Fraction:

[tex]\bold{1\displaystyle\frac{1}{2}}[/tex]

Hence, the value of x is:

[tex]\huge\boxed{\boxed{\mathfrak{\star{Answer:{\boxed{-\frac{3}{2} }}}}}}[/tex]

Hope everything is clear.

Let me know if you have any questions!

#KeepLearning

#NeverGiveUp

[tex]\rm{A~teen~who~never~gives~up}[/tex]

Answer:

3

7

last one doesn't even make sense

The scale drawing of Julio's kitchen would change the kitchen size

The actual area is 243 square feet

The parameters are given as:

Start by converting the dimensions to feet using the scale ratio

The area is then calculated as:

Actual Area = Actual length * Actual Width

This gives

Actual Area =18 feet * 13.5 feet

Evaluate the product

Actual Area = 243 square feet

Hence, the actual area is 243 square feet

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ur mom

Step-by-step explanation:

Answer: 2 units.

Step-by-step explanation: When you graph the points given, it gives you this shape in the image below.  The hypotenuse (longest side of triangle) is found by doing the following:

a^2 + b^2 = c^2, where a and b are the legs (the other sides of the triangle) and c is the hypotenuse.

5^2 + 2^2 = 29.

√ 29 ≈ 5.38, and that is the length of the hypotenuse.

The shortest side is the bottom side, which is 2 units.  Therefore, that is your answer.

Let me know if this is right! :)

Answer:

12

Step-by-step explanation:

pythagorean theorem