5. What is the solution to the system? *
Captionless Image
6. Explain what your solution means in terms of the scenario. *

Answer:

0.743ml=0.000743

Step-by-step explanation:

Final answer:

To determine the number of shareholders aged 40 and over, subtract the number of shareholders under 40 (55.5% of 91,000) from the total, resulting in 40,495 shareholders who are 40 and over.

Explanation:

The question asks how many shareholders are aged 40 and over in a fast food chain given that 55.5% are under 40 and there are a total of 91,000 shareholders.

First, we must find the number of shareholders under 40: 0.555 × 91,000 = 50,505 shareholders. Next, we subtract this from the total number of shareholders to find the number of shareholders aged 40 and over: 91,000 - 50,505 = 40,495 shareholders.

Therefore, 40,495 shareholders are aged 40 and over.

Answer:

[tex]\cos B=0.4[/tex]

Step-by-step explanation:

Given

[tex]\Sin A=0.4=\frac{4}{10}=\frac{2}{5}\\\\In\ right\ triangle\\\\\sin A=\frac{Perpendicular}{Hypotenuse}=\frac{BC}{AB}=\frac{2}{5}\\\\Then\ \ \cos B=\frac{Base}{Hypotenuse}=\frac{BC}{AB}=\frac{2}{5}=0.4[/tex]

Answer:

Part a)

[tex]c=9.3\ units\\b=7.2\ units[/tex]

Part b) [tex]cos(B)=0.4[/tex]  see the explanation

Step-by-step explanation:

The correct question is

In right triangle ABC, C is the right angle. Given measure of angle A = 40 degrees and a =6

Part a) which of the following are the lengths of the remaining two side, rounded to the nearest tenth?

Part b) Which of the following is cos B if sin A=0.4?

see the attached figure to better understand the problem

Part a)

step 1

Find the length of side c

Applying the law of sines

[tex]\frac{a}{sin(A)}=\frac{c}{sin(C)}[/tex]

we have

[tex]a=6\ units\\A=40^o\\C=90^o[/tex]

substitute

[tex]\frac{6}{sin(40^o)}=\frac{c}{sin(90^o)}[/tex]

solve for c

[tex]c=\frac{6}{sin(40^o)}=9.3\ units[/tex]

step 2

Find the length of side b

In the right triangle ABC

[tex]tan(40^o)=\frac{BC}{AC}[/tex] ----> by TOA (opposite side divided by the adjacent side)

substitute the values

[tex]tan(40^o)=\frac{6}{AC}[/tex]

[tex]AC=\frac{6}{tan(40^o)}=7.2\ units[/tex]

therefore

[tex]b=7.2\ units[/tex]

Part b) we know that

If two angles are complementary, the cofunction identities state that the sine of one equals the cosine of the other and vice versa

In this problem

Angle A and angle B are complementary

therefore

the sine of angle A equals the cosine of angle B

we have

sin(A)=0.4

so

cos(B)=0.4

Final answer:

To solve the equation -2.5(4x - 4) = -6, distribute -2.5 to the terms inside the parentheses, isolate the variable, and solve for x.

Explanation:

To solve the equation -2.5(4x - 4) = -6, we can start by distributing -2.5 to the terms inside the parentheses:

-10x + 10 = -6

Next, we can isolate the variable by subtracting 10 from both sides:

-10x = -16

Finally, we can solve for x by dividing both sides by -10:

x = -16/-10

Therefore, x = 1.6.

Answer:

The answer is

[tex] \frac{48}{64} [/tex]

Step-by-step explanation:

Equivalent fractions are set of fractions which have the same value when simplified.

The equivalent fraction to 6/8 whose numerator is 16 less than its denominator can be obtained through two basic methods below.

Method 1

Multiply the numerator and denominator by 8 respectively.

[tex] \frac{6}{8} = \frac{6 \times 8}{8 \times 8} = \frac{48}{64} [/tex]

The numerator being 16 less than the denominator is:

[tex]48 - 64 = - 16[/tex]

Method 2

Find the equivalent fraction to 6/8 whose numerator is 16 less than its denominator by continuous multiplication approach. In other words, multiply 6/8 till you arrive at an equivalent fraction whose numerator is 16 less than its denominator. Simply multiply 6/8 by 2, 3, 4, 5, 6, 7, 8. Thus:

[tex] \frac{6}{8} = \frac{12}{16} = \frac{18}{24} = \frac{24}{32} = \frac{30}{40} = \frac{36}{48} = \frac{42}{56} = \frac{48}{64} [/tex]

The difference between the numerator and denominator of the equivalent fractions are: -2, -4, -6, -8, -10, -12, -14, -16

Hence, 48/64 is the equivalent fraction to 6/8 whose numerator and denominator difference is less than 16.

That is,

[tex] \frac{6}{8} = \frac{48}{64} [/tex]

Such that 48 - 64 = -16.

The fraction equivalent to 6/8 with a numerator 16 less than the denominator is 48/64, which simplifies to 3/4.

To find an equivalent fraction to 6/8 where the numerator is 16 less than the denominator, we use an equation to represent the relationship between the numerator (N) and the denominator (D): N = D - 16. Since 6/8 can be simplified to 3/4 by dividing both the numerator and denominator by 2, we set up the following equation: N/D = 3/4.

By substituting N with (D - 16), we get (D - 16)/D = 3/4. To find the value of D, we cross multiply: 4(D - 16) = 3D. Solving for this, we have 4D - 64 = 3D, and therefore D = 64. Since N is 16 less than D, N = 64 - 16, which gives us N = 48. So, the fraction we are looking for is 48/64.

We can check that 48/64 is indeed equivalent to 3/4 by simplifying. Dividing both numerator and denominator by 16, we get 48/64 = 3/4. Thus, the student's fraction is 48/64 which simplifies to 3/4.

Answer:

8c² + 66c + 16

Step-by-step explanation:

Given

(c + 8)(8c + 2)

Each term in the second factor is multiplied by each term in the first factor, that is

c(8c + 2) + 8(8c + 2) ← distribute both parenthesis

= 8c² + 2c + 64c + 16 ← collect like terms

= 8c² + 66c + 16

Answer:

answer is a

look at picture

Answer:

[tex]\$14,187.27[/tex]

Step-by-step explanation:

we know that

In this problem we have a exponential decay function of the form

[tex]y=a(1-r)^x[/tex]

where

y ----> is the value of the boat in dollars

x ---> is the number of years

r ---> is the percent rate of change

a ---> is the initial value or y-intercept

we have

[tex]a=\$19,300\\r=5\%=5/100=0.05[/tex]

substitute

[tex]y=19,300(1-0.05)^x[/tex]

[tex]y=19,300(0.95)^x[/tex]

For x=6 years

substitute the value of x in the exponential function

[tex]y=19,300(0.95)^6\\y=\$14,187.27[/tex]

Answer:

a 90° clockwise rotation about the origin

a 180° rotation about the origin

a 90° counterclockwise rotation about the origin

Step-by-step explanation:

Transformations are done on a Cartesian Plane, which is the grid with four quadrants. (See picture) Each quadrant is 90°, so two quadrants is 180°.

When you rotate counterclockwise it is like in the picture. When you want to rotate clockwise, it's the other way.

When we rotate 180°, it does not matter if it is counterclockwise or clockwise because the result is the same (both move two quadrants).

We can imagine an example to help us solve the problem. Let's say we are rotating an object starting in first quadrant. (Upper right quadrant).

Find out which quadrant the object ends up with each instruction:

FROM THE PICTURE:

"a 90° counterclockwise rotation about the origin (Q2) and then a 180° rotation about the origin"

End: Quadrant 4

"a reflection across the x-axis (Q4) and then a reflection across the y-axis"

End: Quadrant 3

"a 90° clockwise rotation about the origin (Q4) and then a rotation 180° about the origin"

End: Quadrant 2

FROM YOUR LIST:

"a 90° counterclockwise rotation about the origin " Quadrant 2

"a 180° rotation about the origin " Quadrant 3

"a 90° clockwise rotation about the origin" Quadrant 4

Match each ending quadrant from your list with the same ending quadrant from the picture.

The order that you should put your list into the boxes is:

a 90° clockwise rotation about the origin

a 180° rotation about the origin

a 90° counterclockwise rotation about the origin

Answer:

C

Step-by-step explanation:

You can already walk 0.9 of a mile in 3/8 so it cannot be A or B

C is the most reliable because even if you multiple the 0.9 by 3 so it is a little bit over a mile it is still closer to 2.4

Answer:

2.5 minutes or 150 seconds

Step-by-step explanation:

Time = Distance / speed

300/2 = 150.

150 seconds, or 2 and a half minutes

Answer:

5.5 pounds of seeds

Step-by-step explanation:

22 pounds seeds = 4-acre field

(x) pounds seeds = 1-acre(per acre)

x= 22/4

 = 5.5 pounds of seeds

Answer:

The area of trapezoid PQRS is 125 square units

Step-by-step explanation:

The picture of the question in the attached figure

we know that

If trapezoid PQRS with parallel sides PQ and RS is divided into four triangles by its diagonals PR and QS , intersecting at X, then the area of triangle PSX is equal to that of triangle QRX, and the product of the areas of triangle PSX and triangle QRX is equal to that of triangle PQX and triangle RSX

Let

A_1 ----> the area of triangle PSX

A_2----> the area of triangle QRX

A_3 ---> the area of triangle PQX

A_4 ---> the area of triangle RSX

[tex]A_1*A_2=A_3*A_4[/tex]

[tex]A_1=A_2[/tex]

so

[tex]A_1^2=A_3*A_4[/tex]

we have

[tex]A_3=20\ units^2\\A_4=45\ units^2[/tex]

substitute

[tex]A_1^2=(20)(45)\\A_1^2=900\\A_1=30\ units^2[/tex]

The area of trapezoid is equal to

[tex]A=A_1+A_2+A_3+A_4[/tex]

substitute

[tex]A=30+30+20+45=125\ units^2[/tex]

Final answer:

The area of trapezoid PQRS is found by adding the areas of triangle PQX (20 square units) and triangle RSX (45 square units) together, which equals 65 square units.

Explanation:

The area of trapezoid PQRS can be found by summing up the areas of triangle PQX and triangle RSX. Since diagonals PR and QS intersect at point X, both triangles share the same height, which is the perpendicular distance from point X to the bases PQ and RS. Thus, the area of trapezoid PQRS is simply the sum of the areas of the two triangles.

To calculate the area of trapezoid PQRS, we add the area of triangle PQX, which is given as 20, to the area of triangle RSX, which is given as 45. Therefore, the area of trapezoid PQRS is:

Area of trapezoid PQRS = Area of triangle PQX + Area of triangle RSX = 20 + 45 = 65

So, the area of trapezoid PQRS is 65 square units.

Answer:

56 football cards

Step-by-step explanation:

If 5 baseball cards multiplied by 8 is 40, then you multiply the 7 football cards by 8 as well.

7x8=56

The solution set is x = 3, y = 4 (or) x = 3, y = –4.

Solution:

Given system of algebraic equations are

[tex]y^{2}+(x-8)^{2}=41[/tex] – – – – – (1)

[tex]y^{2}-25=-x^{2}[/tex] – – – – – (2)

Expand equation (1) using algebraic identity: [tex](a-b)^2=a^2-2ab+b^2[/tex]

[tex]y^{2}+x^2-16x+64=41[/tex]

subtract 64 from both sides of the equation

[tex]y^{2}+x^2-16x+64-64=41-64[/tex]

[tex]y^{2}+x^2-16x=-23[/tex] – – – – – (3)

Now, to arrange equation (2) in order, add [tex]x^2[/tex] on both sides.

[tex]y^{2}-25+x^2=-x^{2}+x^2[/tex]

[tex]y^{2}-25+x^2=0[/tex]

Add 25 on both sides of the equation,

[tex]y^{2}+x^2=25[/tex] – – – – – (4)

To solve this subtract equation (4) from equation (3)

[tex]\Rightarrow y^{2}+x^2-16x-(y^{2}+x^2)=-23-25[/tex]

[tex]\Rightarrow y^{2}+x^2-16x-y^{2}-x^2=-23-25[/tex]

[tex]\Rightarrow -16x=-48[/tex]

Divide both sides of the equation by –16,

⇒ x = 3

Substitute x = 3 in equation (4), we get

[tex]\Rightarrow y^{2}+3^2=25[/tex]

[tex]\Rightarrow y^{2}=25-9[/tex]

[tex]\Rightarrow y^{2}=16[/tex]

[tex]\Rightarrow y=\pm 4[/tex]

i. e. y = 4 (or) y = –4

The solution set is x = 3, y = 4 (or) x = 3, y = –4.

Answer:

It remained 9/50 of the pie

Step-by-step explanation:

If Janelle ate 82% of the pie, now it remains:

100 - 82 = 18%

Let's convert 18% to fraction:

18% = 0.18 = 18/100

Let's simplify 18/100:

18/100 = 9/50 (Dividing by 2 the original fraction)

It remained 9/50 of the pie

Answer:

bunches up in the middle and tapers off symmetrically at either end

Step-by-step explanation:

By definition a normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Because the data towards the mean is more frequent in occurrence, the graph peaks at the center. The data occurs less frequently at the tail ends of the distribution, thus the shape of the distribution is a bell shape that peaks at the center and tapers off towards the tails.  The key characteristic is that the distribution of data is perfectly symmetrical.

This is why the answer is:

The data depicted in a histogram show approximately a normal distribution if the distribution bunches up in the middle and tapers off symmetrically at either end.

Answer:

x = 29

y = 6

Step-by-step explanation:

Let the two numbers be represented as x and y

x + y = 35

x = 5y - 1

Substitute x as 5y -1 in equation one

5y -1 + y = 35

5y + y -1 = 35

Add 1 to both sides

6y - 1 + 1 = 35 + 1

6y = 36

Divide both sides by 6

6y/6= 36/6

y = 6

Now substitute y as 6 in any of the equations to get x.

Using equation one ,

We have

x + y = 35

x +6 = 35

Subtract 6 from both sides

x + 6 - 6 = 35 - 6

x = 29

Answer:

The answer you have is Correct!

The height of tree is 32 meter

Solution:

Given that,  The sun is at an angle of elevation of 58 degree

A tree casts a shadow 20 meters long on  the ground

The sun, tree and shadow forms a right angled triangle

The figure is attached below

ABC is  a right angled triangle

AC is the height of tree

AB is the length of shadow

AB = 20 meters

Angle of elevation, angle B = 58 degree

By definition of tan,

[tex]tan \theta = \frac{opposite}{adjacent}[/tex]

In this right angled triangle ABC,

opposite = AC and adjacent = AB

Therefore,

[tex]tan\ 58 = \frac{AC}{AB}\\\\tan\ 58 = \frac{AC}{20}\\\\1.6 = \frac{AC}{20}\\\\AC = 1.6 \times 20\\\\AC = 32[/tex]

Thus height of tree is 32 meter

Step-by-step explanation:

We have,,

6x and 2x

To find, the value of x = ?

According to question,

The sum of 6x and 2x is at least 39

∴ 6x + 2x = 39

⇒ 8x = 39

⇒  x = [tex]\dfrac{39}{8}[/tex]

∴ The value of x = [tex]\dfrac{39}{8}[/tex]

Thus, put x = [tex]\dfrac{39}{8}[/tex] I write the sum of 6x and 2x is at least 39 .

Answer:

28/45

Step-by-step explanation:

Solve using cross multiplication.

(7/15) / (4/3) =

28/45

The fraction is already in simplest form

answer:

[tex] \frac{7}{20} [/tex]

explanation:

[tex] \frac{7}{15} \times \frac{3}{4} = \frac{7 \times 3}{15 \times 4} = \frac{21}{60} = \frac{7 \times 3}{20 \times 3} = \frac{7}{20} [/tex]

Answer:

B. right scalene triangle

i am sure about this answer as 90 degree tells us that it is a right angle triangle and as all the measure of angles as well as sides are different it is a scalene triangle.

Option C:

[tex]$\sqrt[5]{34} =34^{\frac{1}{5} }[/tex]

Solution:

Given expression is [tex]\sqrt[5]{34}[/tex].

To write the given expression in rational exponent form.

Using rational exponent rule:

[tex]$\sqrt[n]{a^m} =a^{\frac{m}{n} }[/tex]

i. e. [tex]$\sqrt[\text{root}]{a^\text{power}} =a^{\frac{\text{power}}{\text{root}} }[/tex]

Given  [tex]\sqrt[5]{34}[/tex]

Here, root is 5 and power is 1.

Write it using the rational exponent rule,

[tex]$\sqrt[5]{34} =34^{\frac{1}{5} }[/tex]

Therefore option C is the correct answer.

Hence [tex]$\sqrt[5]{34} =34^{\frac{1}{5} }.[/tex]

Answer: 34^1/5

Step-by-step explanation:

Answer:

f(-9) = -23

Step-by-step explanation:

Step 1:  Identify the function

f(x) = 3x + 4

Step 2:  Set x to -9 in the function

f(-9) = 3(-9) + 4

Step 3:  Multiply

f(-9) = -27 + 4

Step 4:  Add

f(-9) = -23

Answer:  f(-9) = -23

Answer:

       _

-0.416       or for rounded     0.417

Step-by-step explanation:

when you multiply  -1/4 and 5/3 you will get a repeating decimal so what you will do is ether round it or put a line on top of the 6 showing that the number six never ends so when you round it you should round the thousandths plae making it -0.417

Good evening,

Answer:

Step-by-step explanation:

Two angles are supplementary if the sum of their measures is equal to 180°

then the measurement of an angle that is supplementary to an angle that measures 80° is :

180 - 80 = 100°

Answer:

a. 1/10

b. 4/10

c. 20

Step-by-step explanation:

There are 10 equal sections.

a. 1 section is labeled "Large Prize", so the probability of winning a large prize is 1/10.

b. 1 section is labeled "Large Prize" and 3 sections are labeled "Small Prize", so there's 4 prize section.  Therefore, the probability of winning a prize is 4/10.

c. Each person has a 4/10 chance of winning a prize.  So if there are 50 people, we would expect 4/10 × 50 = 20 people to win a prize.

Answer:

  A)  The 75 is the initial number of cells, and the 2 indicates that the number of cells doubles every minute

Step-by-step explanation:

When x=0 (no minutes have elapsed), the value of the function is ...

  f(0) = 75(2^0) = 75(1) = 75 . . . . the initial number of cells

As x increases by 1 (minute), the number of cells is multiplied by 2, so the 2 is the multiplier each minute. It indicates the number doubles. ("double" = "multiply by 2")

x is not defined, but for the function to make any sense, it must represent elapsed minutes.

Answer:

Step-by-step explanation:

Carlo's outcome will be the greatest if Sorin's number will be the highest and Jiao's number is the lowest.

Sorin choose a three digit number, the highest three digit number is 999.

After doubled the number, 999, the outcome will be 1998.

Jiao chooses two-digit number, the lowest two-digit number is 10.

Hence, the greatest number that Carlo can get is (1998 - 10) = 1988.

Final answer:

The greatest number Carlos can get is 1988, which is found by doubling the largest three-digit number, 999, to get 1998, and then subtracting the smallest two-digit number, 10.

Explanation:

To find the greatest number Carlos can get, we must consider the largest possible three-digit number that Sorin could double and the smallest possible two-digit number Jiao could choose.

The largest three-digit number is 999. When doubled, it becomes 1998. The smallest two-digit number is 10. Therefore, Carlos' greatest possible number is obtained by subtracting the smallest two-digit number from Sorin's doubled number:

1998 - 10 = 1988

Hence, the greatest number Carlos can get is 1988.