If f(x) = -x^2 – 1, and
g(x) = x + 5, then
g(f (x)) = [? ]x^2+[ ]x + [ ]

Answer:

27.13 ounces of one solution and 57.87 ounce of other solution

Step-by-step explanation:

Considering 'x' no. of ounces of one solution and 'y' no. of ounces of other solution.

Lets form the equations according to the given data.

-> she wishes to obtain 85 ounces by combining both solutions

x+y= 85

x = 85- y -->eq(1)

-> by combining a 72% acid solution with a 25% acid solution  

0.72x + 0.25 y = 0.4 x 85 --> eq(2)

Substituting value of eq(1) in eq(2)

0.72(85-y) + 0.25 y = 34

61.2 - 0.72y + 0.25y = 34

-0.47y= 34-61.2

y= 27.2/0.47

y= 57.87 ounces

Plugging in eq(1)

eq(1)=> x = 85- 57.87

x= 27.13 ounces

Therefore, Misty should use 27.13 ounces of one solution and 57.87 ounce of other solution

Answer:

= 150°

Step-by-step explanation:

Since the polygons are regular, certain mathematical assumptions would help us here.

A square is a quadrilateral with all it's 4 sides equal and all it's angles equal.

Sum of angles of a regular quadrilateral = 360.

Therefore, a single angle = 360/4

= 90°.

The Triangle is adjacent to the side of the square. We will thus assume it's an Equilateral triangle.

For an equilateral triangle, all it's 3 angles = 180.

A single angle = 180/3

= 60°.

With this,

Angle ABC = 90° + 60=

= 150°

Answer:

The amount of money in the account after 8 years is $15,059

Step-by-step explanation:

The formula for compound interest, including principal sum, is

[tex]A=P(1+\frac{r}{n})^{nt}[/tex] , where

∵ $9500 is invested at 5.8%, compounded quarterly

∴ P = 9500

∴ r = 5.8% = [tex]\frac{5.8}{100}[/tex] = 0.058

∴ n = 4 ⇒ compounded quarterly

∵ The amount of money will be in the account for 8 years

∴ t = 8

Substitute all of these value in the formula above

∵ [tex]A=9500(1+\frac{0.058}{4})^{4(8)}[/tex]

∴ [tex]A=9500(1.0145})^{32}[/tex]

∴ A = 15058.7613 dollars

- Round it to the nearest dollar

∴ A = 15059 dollars

The amount of money in the account after 8 years is $15,059

Answer:

Step-by-step explanation:

Please share the answer choices next time.

The simplest diagram of a 30-60-90 triangle indicates leg lengths of 1 and √3 and hypotenuse 2.  Thus, the desired ratio is √3/2.  This is the sine of 60° and also the cosine of 30°

Answer: 3\3 :6 , \3:2 and 3 :2/3

Step-by-step explanation:

Answer:

10/13 = 76.92%

Step-by-step explanation:

The question is missing some information because the underline is missing.

If we make table based on if the letter upper case (A) or lower case(a), and if the letter underlined(B) vs not underlined(b) the data will be:

             A          a

B           4           3         7

b           3           3         6

total      7          6

There are total of 13 letter there. The calculation will be:

P(A or B) = P(A) + P (B) - P(A and B) = (7 + 7 -4) / 13= 10/13 = 76.92%

Answer:

The density of salt solution is [tex]4.94\times 10^{-3}\ g/cm^3[/tex].

Step-by-step explanation:

Given that,

Volume of certain solution, V = 7.5 litres

Mass of salt in solution, m = 37 grams

We know that, [tex]1\ L=1000\ cm^3[/tex]

We need to find the density of salt in the solution. The density of salt is given by mass per unit volume. The formula can be written as:

[tex]d=\dfrac{m}{V}\\\\d=\dfrac{37\ g}{7.5\times 10^3\ cm^3}\\\\d=4.94\times 10^{-3}\ g/cm^3[/tex]

So, the density of salt solution is [tex]4.94\times 10^{-3}\ g/cm^3[/tex].

Answer:4.9

Step-by-step explanation:

Answer:

55 games.

Step-by-step explanation:

We have been given that Enzo wins 5 tickets from every game, and Beatriz wins 11 tickets from every game. When they stopped playing games, Enzo and Beatriz had won the same number of total tickets. We are asked to find the minimum number of games that Enzo could have played.

To solve our given problem, we need to find least common multiple of 1 and 55.

We know that least common multiple of two numbers is smallest umber, which is divisible by both numbers.

We know that 5 and 11 are prime numbers, so there LCM would be product of both numbers.

[tex]5\times 11=55[/tex]

Therefore, Enzo could have played 55 games at least.

Answer:

16 children attended the play

Step-by-step explanation:

Since one adult brought four children. The cost of their tickets should be:

($4×1) + ($2×1)

= 4+8

= $12

Since the remaining adults brought 2 children each, it means that each of the remaining adults will pay the cost of three tickets (1 for themselves and 2 for their children) which is:

($4×1) + ($2×2) = $4 + $4 = $8.

Since total cost of tickets for adults and children = $60, we will subtract $12 from $60 in order to know the cost of the tickets for the remaining adults and their children.

$60 - $12 = $48

Each of the remaining adults paid $8 as ticket cost for themselves and their kids. If the adults that brought only 2 kids paid a combined $48, then the number of adults that brought 2 kids each

= $48/$8

= 6 adults.

If each of these 6 adults brought 2 kids each, then the number of children that they brought = 2 × 6 = 12

We now add this to the four children of the first adult

12 + 4 = 16

Therefore the number of children that attended the play = 16

The problem is solved by setting up and solving equations, determining that 16 children attended the play.

The subject of this problem is setting up and solving equations. The given information can be translated into equations. Four children and one adult make up one group. For this group, the total cost is $4 (for the adult) + $2 * 4 (for the children) = $12. For the remaining adults and children, we know each adult brought 2 children and the cost would be $4 (for the adult) + $2 * 2 (for the children) = $8 per group. We know the total cost was $60. So, subtract the $12 from the first group, which leaves $48. As we know each of the remaining groups cost $8, we divide $48 by $8 to find that there were 6 more groups. Each of these groups consists of 1 adult and 2 children, so there were 6 * 2 = 12 children in these groups. Added to the original 4 children, that makes 16 children in total.

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Answer: The last one (C)

Step-by-step explanation: Use the rule to convert  

15

1

3

to a radical, where  

a

=

15

,  

x

=

1

, and  n = 3 .

3 √ 15

9514 1404 393

Answer:

  A, D, E

Step-by-step explanation:

Given:

  A triangular prism 7 m high with a base triangle that has a base of 8 m and a height of 14 m.

Find:

  3 steps among those listed that should be taken to compute the volume.

Solution:

The listed steps are ...

  (a) Use the formula A = one-half b h to find the area of the base.

  (b) Use the formula A = b h to find the area of the base.

  (c) The area of the base, A, is One-half (7) (8) = 28 meters squared.

  (d) The area of the base, A, is One-half (8) (14) = 56 meters squared.

  (e) The volume of the prism, V is (56) (7) = 392 meters cubed

__

The formula for the volume is ...

  V = Bh . . . . where B is the area of the base, and h is the prism height

The formula for the area of a triangle is ...

  A = 1/2bh . . . . where b is the base of the triangle and h is its height

We need the area of the triangular base before we can use the volume formula, so the first step is (a). The next step is to fill in values in that formula, so the second step is (d). Finally, we fill in values in the volume formula, so the third step is (e).

Of the steps listed, we should use steps (a), (d), (e).

Answer:

4

Step-by-step explanation:

Answer:

21

(4)

Step-by-step explanation:

Answer:.74 is the higher number

Step-by-step explanation: i'm bad at explaining things but i hope this helps

The number 0.74 is larger than 0.084. This can be determined by comparing the numbers from left to right.

The question asks for the larger number between 0.74 and 0.084. When comparing decimal numbers, look at each digit from left to right. In our case, the first number has 7 in the tenths place, while the second number has 0. Therefore, 0.74 is greater than 0.084. As a general rule in mathematics, larger numbers often have more digits to the left of the decimal point or larger digits in the most leftward position for numbers to the right of the decimal point.

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Answer:

Ariel will make a bigger batch.

Step-by-step explanation:

Scott- Every 2 cups Almonds = 3 cups raisins

so 6 cups almonds = 9 cups raisins

6+9= 15

Scott's batch- 15 cups

Ariel- Every 3 cups Almonds = 5 cups sunflower seeds

so 6 cups almonds = 10 cups sunflower seeds

6+10= 16

Ariel's batch- 16 cups

16 > 15 so Ariel's is bigger.

Ariel makes the larger batch of snack mix

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Equation for Scott :

Number of cups of Almonds = 2 cups

Number of cups of Raisins for 2 cups of almonds = 3 cups

Number of cups of almonds = 6 cups

Number of cups of raisins for 6 cups of almonds = 3 x 3

                                                                                 = 9 cups

So , total number of cups by Scott =
Number of cups of almonds + Number of cups of raisins for 6 cups of almonds

Total number of cups by Scott =  6 + 9 cups

The batch of snack mix by Scott has 15 cups

Equation for Ariel :

Number of cups of Almonds = 3 cups

Number of cups of sunflower seeds for 3 cups of almonds = 5 cups

Number of cups of almonds = 6 cups

Number of cups of raisins for 6 cups of almonds = 5 x 2

                                                                                 = 10 cups

So , total number of cups by Ariel =
Number of cups of almonds + Number of cups of sunflower seeds for 6 cups of almonds

Total number of cups by Ariel =  6 + 10 cups

The batch of snack mix by Ariel has 16 cups

Therefore , the batch mix of snack by Ariel is more than the batch mix of snack by Scott

Hence , Ariel makes the larger batch

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Answer:

x = 3.5

perimeter of each figure = 54

Step-by-step explanation:

Perimeter of square:  4(3x + 3)       12x + 12

Perimeter of equilateral triangle:  3(5x + 0.5) = 15x + 1.5

Solve for x:  12x + 12 = 15x + 1.5

Grouping like terms results in 10.5 = 3x, which leads to x = 3.5.

Each polygon has a perimeter of 12x + 12, which here is 12(3.5) + 12 = 54

x = 3.5

perimeter of each figure = 54

Answer:

1 is 7/4

2 is 7/2

3 is 11.0

Step-by-step explanation:

they all the right answer thank me later

Answer:

the guy above is right on edge 2021

Step-by-step explanation:

i got the question right because of them

Answer:

There is insufficient evidence to support the claim that  it's not a surprising value given that only 45​% of all its employees are women

Step-by-step explanation:

-Given that [tex]p_o=0.45, n=47, x=20[/tex]

-We state our hypothesis as:

[tex]H_o:p=0.45\\\\H_a:p\neq 0.45[/tex]

#We apply the one-proportion z-test to test the claim about the one population proportion.

-The sample proportion is calculated as:

[tex]\hat p=\frac{x}{n}\\\\=\frac{20}{47}\approx0.4255[/tex]

#We determine the value of the test statistic as:

[tex]z=\frac{\hat p-p_o}{\sqrt{\frac{p_o(1-p_o}{n}}}\\\\=\frac{0.4255-0.45}{\sqrt{(0.45\times 0.55)/47}}\\\\=-0.3376[/tex]

#We determine the p-value using the normal probability table:

[tex]P=P(Z<-0.3376 \ or \ Z>0.3376)\\\\=2P(Z<-0.3376)\\\\=2\times 0.32636 \\\\=0.6527[/tex]

[tex]P>0.05[/tex] =>Fail to reject [tex]H_o[/tex]

There is insufficient evidence to support the claim that  it's not a surprising value given that only 45​% of all its employees are women

To test the claim that female representation among executives is in line with company-wide figures, we perform a hypothesis test. While the observed female proportion in the local branch is below the stated company-wide figure, further analysis using test statistics and p-value comparison with a level of significance (for instance, 0.05) is necessary to decide if this difference is statistically significant.

The subject of this question is a hypothesis test related to population proportions. To test the hypothesis that the percentage of female executives in the local branch is not significantly below the overall percentage within the company, we establish the null hypothesis: H0: The proportion of female executives is equal to or greater than 45%, and the alternative hypothesis: H1: The proportion of female executives is less than 45%. Using the given figures, we can calculate the observed proportion of female executives in the local branch as 20/47 = 0.4255 or roughly 42.55%, which is less than 45%. Given the borderline nature of the result, we would typically proceed by calculating the test statistic and looking up the corresponding p-value. If the p-value is less than our level of significance (say α = 0.05), we would reject the null hypothesis, indicating that the imbalance is statistically significant. If not, we fail to reject the null hypothesis, implying that there isn't enough evidence to prove a significant disproportion. Ultimately, the final conclusion needs the actual p-value.

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Answer:

You can use it in different ways

Step-by-step explanation:

sometimes it may be in correct as it is not a 100 percent way to get and answer

You do not use the completing the square method when the quadratic coefficient is not a perfect square, when the middle coefficient is odd, or when dealing with complex numbers. The quadratic formula is often more efficient under these circumstances.

The completing the square method is typically not used in certain circumstances in solving quadratic equations. For example, it is not the best approach when the quadratic coefficient (the 'a' term when the quadratic is in the form ax^2+bx+c=0) is not a perfect square and cannot be easily made into one. Additionally, this method is often avoided if the middle coefficient (the 'b' term) is odd, making it cumbersome to deal with fractional or decimal numbers when completing the square.

Instead, it might be more efficient to use the quadratic formula, which can handle any type of quadratic equation. The quadratic formula, x equals minus 'b', plus-or-minus the square root of 'b' squared minus four 'a' 'c', all over two 'a', provides a direct solution without the need for making any initial transformations to the equation. This formula is also preferred when the equation has coefficients that do not lend themselves to simple arithmetic or when the equation is not easily factorable.

In contrast, the completing the square method is best when dealing with integrals in calculus or when you need the equation in vertex form for analyzing the properties of a parabola. In such scenarios, completing the square provides additional insight into the problem at hand.

Answer:

the dimensions are;

Width = 14.5 ft

Length = 25.5 ft

Step-by-step explanation:

We are told that width is 11 feet less than length. Let Width be W and Length be L.

Thus;

W = L - 11

Area of rectangle is given by;

Area; A = 2W + 2L

Putting L - 11 for width, we have;

Area = 2(L - 11) + 2(L)

A = 2L - 22 + 2L

A = 4L - 22

Length = L

Width = W

Area = A

A =4L-22

We are told that Area is 80 square feet. Thus;

80 = 4L -22

Add 22 to both sides to give;

102 = 4L

Divide both sides by 4 to give;

102/4 = 4L/4

L = 25.5

Recall that; W = L - 11

Thus;

W = 25.5 - 11 = 14.5

So the dimensions are;

Width = 14.5 ft

Length = 25.5 ft

Two complementary angles equal 90.

If angle 1’s complementary angle is 80, then angle 1 is 10 (90-80=10)

The three angles of a triangle need to equal 180.

Angle 3 = 180 - angle 1 - angle 2

Angle 3 = 180 - 10 - 80 = 90

Angle 3 = 90 degrees

Answer:

c

Step-by-step explanation:because ive done this assignment and got 100

The value of x from the given figures is 30 inches. Therefore, option C is the correct answer.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".

Given that, the two figures are proportional.

Here, 36/12 =x/10

x/10 =3

x=30 inches

Therefore, option C is the correct answer.

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Answer:

a) The movie is 2 hours and 10 minutes long.

b) Check Explanation

c) The second showing starts at 6:45 p.m. The movie lasts 2 hours and 10 minutes, so it ends at 8:55 p.m. So, the second showing will not be over by 8:45 p.m.

Step-by-step explanation:

The first showing starts at 3:45 pm, the second showing starts at 6:25 pm and there's a break of (1/2) hour between the showings,

To now find how long the video was.

The length of the film.is the difference between the times 6:25 pm and 3:45 pm while also removing the (1/2) hour break time too.

The time between 3:45 pm and 6:25 pm is 2 hours, 40 minutes. Now removing the (1/2) hour break from this time, we are left with 2 hours, 10 minutes.

Hence, the movie is 2 hours and 10 minutes long.

b) To use the number line, we would convert the times into hours, that way, it works.

The time 3:45 is 3.75 on the number line, the time, 6:25 is 6.4167 on the number line. And the (1/2) hour break is a length of 0.5 on the number line.

Working backwards from 6.4167, we go back a length of 0.5 and land on 5.9167.

We can then calculate the length of time between 3.75 and 5.9167

5.9167 - 3.75 = 2.16667 hours

Which directly translates to 2 hours and 10 minutes as obtained in (a)

c) The second showing started 20 minutes late. Will the second showing be over by 8:45 p.m.? Complete the explanation why your answer is reasonable.

The second showing is known to initially start at 6:25 pm, but now, there's a delay of 20 minutes, which pushes the start time to 6:45 pm and the movie lasts for 2 hours and 10 minutes as calculated in (a).

So, 2 hours and 10 minutes from 6:45 pm gives 8:55 pm. So, the second showing will end by 8:55 pm if it starts 20 minutes late.

And the second showing will not be over by 8:45 pm.

Hope this Helps!!!

Answer:5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

27,488.94 cubic feet

Step-by-step explanation:

I think thats it

Amount of water will fill the cylindrical aquarium is 11083.54 cubic feet

"A cylinder is a closed solid that has two parallel (usually circular) bases. The two circular bases are joined by a curved surface, at a fixed distance from the center. "

Formula for volume of cylinder

V = [tex]\pi r^{2}h[/tex]

We have,

V = [tex]\pi[/tex](252)(14)

By comparing two equations of volume

[tex]r^{2}[/tex] [tex]= 252[/tex]

⇒ [tex]r = \sqrt{252}[/tex]

⇒ [tex]r = 15.875[/tex]

Radius of base(circle) = 15.875

Height of cylindrical aquarium [tex]h = 14[/tex]

Amount of water will fill the cylindrical aquarium

V = [tex]\pi (252)(14)[/tex]

V = 11083.539 cubic feet

V = 11083.54 cubic feet (nearest hundredth)

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Answer:

.027(a^3)

Step-by-step explanation:

The volume of a cube is s^3, where s is the sidelength

We plug in .3a for s, because the sidelength has been reduced to 30% of a.

We get (.3a)^3 = .027(a^3)

Answer:

.027(a^3)

Step-by-step explanation:

Answer:

84 pounds per square inch

Step-by-step explanation:

 Extracting the key information from the question:

*** Volume of a gas is inversely proportional to pressure of the gas.

*** A balloon is filled with  228 cubic inches of a gas at a pressure of 14 pounds per square inch.

*** Volume is then decreased to 38 cubic inches. we are required to find the new pressure of the gas.

    Since volume is inversely proportional to pressure, then:

     V = k × (1/p)

      V = k/p

V = volume, p= pressure, k = mathematical constant

Since, V = 228 cubic inches, P = 14 pounds per square inches, k = ?

 Substituting appropriately, we have:

     228/1 = k/14

  cross multiply

K = 228 × 14 = 3192

 Using the same formula, we can calculate the new pressure of the gas since we know our mathematical constant and the volume it was decreased to.

  V = k/p

Here, volume = 38, k = 3192

 We now have:

   38/1 = 3192/p

 Cross multiply

 38 × p = 3192

   p = 3192/38

   p = 84 pounds per square inch.

 The new pressure of the gas after decrement of the volume= 84 pounds per square inch

When the temperature stays the same, the new pressure of the gas if the volume is decreased is 84 pounds per square inch.

Given the following data:

To find the new pressure of the gas if the volume is decreased:

Translating the word problem into a mathematical expression, we have;

[tex]V \alpha \frac{1}{P} \\\\V = \frac{k}{P}[/tex]

Where:

First of all, we would determine the constant of proportionality.

[tex]k = VP\\\\k = 228 \times 14[/tex]

k = 3,192

To find the new pressure:

[tex]P = \frac{k}{V} \\\\P = \frac{3192}{38}[/tex]

New pressure, P = 84 pounds per square inch

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Answer:

(x - 7) (x - 1) or option a

Step-by-step explanation:

(x - 7) (x - 1) =

x² - 7x - x + 7 =

x² - 8x + 7

Answer: 2 decimal digits

Step-by-step explanation:

When multiplying decimals, placement of the decimal point is very important. Since there is one decimal digit in each factor, there must be two decimal digits in the product. This is because tenths x tenths = hundredths

Hope this helps and good luck! :)

Answer:

Depends on the question

For example 2x1.3=2.6

or 2.3x 5.2343= 12.03889

To answer your question It could range between 0-2

Step-by-step explanation: