Find the missing values in the ratio table. Then write the equivalent ratios.

Answer:

  (b)  35.5w + 136.45 = 455.95; w = 9

Step-by-step explanation:

You want an equation to determine how many weeks, w, you must babysit to earn $455.95 at the rate of $35.50 each week, having already saved $136.45.

If you earn $35.50 each week for w weeks, your total earnings will be ...

  35.50w

When that amount is added to the amount you already have, $136.45, the sum is ...

  35.5w +136.45

You want that total to be $455.95, which gives you the equation ...

  35.5w +136.45 = 455.95

To solve this 2-step equation, subtract the left-side constant:

  35.5w = 319.50

The second step is to divide by the coefficient of the variable:

  w = 319.50/35.5

  w = 9

Answer:

18%

Step-by-step explanation:

percentage discount is calculated as

[tex]\frac{discount}{original}[/tex] × 100%

here discount = $50 - $41 = $9 , then

% discount = [tex]\frac{9}{50}[/tex] × 100% = 9 × 2% = 18%

Using the triangle rule, the option B can form a triangle.

In the given question,

We have to choose the correct segment from the given segment,  which group of segments can form a triangle.

The given options are

A. 3, 10, 14

B. 8, 7, 13

C. 3, 2, 5

D. 20, 7, 13

To check which segment form a triangle we check that sum of two sides is always greater than the third side.

Now checking the first option.

The points is 3,10,14

When we add 3 and 10 we get 13 which is not greater than the 14. So the option A is not form a triangle.

Now checking the second option.

The points is 8,7,13

When we add 8 and 7 we get 15 which is greater than the 13. Similarly when we add 13 and 7 we get 20 which is also greater than the 8. Similarly when we add 8 and 13 we get 21 which is also greater than the 7. So the option B can form a triangle.

Since we get the right answer so we didn't check further option. The way of checking the remaining option is same.

Hence, the option B can form a triangle.

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Answer:B 3 1/4 + (5/8)

D 3 1/4 + (+5/8)

Step-by-step explanation:

Calculation

an expression is the combination of numbers and operators like +, - * or /

If we have any equal sign then it is an equation .

Given expression is :

to find out equivalent expression  we  remove the parentheisis  by multiplying negative inside the parenthesis

Negative  times negative becomes positive

first fraction is positive . So it remains the same

Multiply negative inside the parenthesis . Negative times negative is positive

so, the equivalent expressions are

(C) represents a function with the same rate of change at the function       [tex]y = \frac{7}{4}x+3[/tex].

Given equation,

[tex]y = \frac{7}{4}x+3[/tex]

Slope = m = 7/4

Slope = (x2-x1)/(y2-y1)

Now we will check every option and find slope which we be 7/4.

(A) A(1,0) and B(5,-4)

    Slope = (-4-0)/(5-1)

               = -4/4

               = -1

               ≠ m

(B) A(-1,1) and B(0,4)

     Slope = (4-1)/(0+1)

                = 3/1

                = 3

                ≠ m

(C) A(-4,-6) and (0,1)

    Slope = (1+6)/(0+4)

               = 7/4

               = m

(D) A(0,-2) and B(-4,5)

    Slope = (5+2)/(-4-0)

               = 7/-4

               = -7/4

               ≠ m

Hence, only (C) satisfies the situation.

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These triangles can be proven congruent by using S-A-S rule.

What is congruent triangles?

Two triangles are same to be congruent if all 3 corresponding sides ar equal and every one the 3 corresponding angles ar equal in measure. These triangles will be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with one another. The symbol of congruence is’ ≅’.

Main body:

In ΔABC and ΔXYZ

AC = XZ   ---(1)

∠C = ∠ Z    ---(2)

BC = YZ    ---(3)

using 1, 2 ,3  we can prove that  ΔABC and ΔXYZ are congruent.

Hence ΔABC and ΔXYZ  are congruent.

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Answer: 6.16

minus all the values from 30

Answer:

$6.16

Step-by-step explanation:

30-6.97-11.37-5.5

=6.16

The range from the given table is 9, the population variance is 18.56, and the population standard deviation is 4.30.

Given the value:

xi         10     20      11        17       15     8     7     16       19    15     Total = 138

xi^2    100   400    121   289    225   64   49   256   361   225  Total = 2090

From the above, we get

n =10, ∑xi = 138, ∑xi^2 = 2090

(a) For the range:

Here, the smallest value = 10, and largest value = 19

Therefore, Range = Largest value - Smallest value

Range = 19 - 10 = 9

(b) For population variance:

For mean:

Mean of x = ∑xi/n = 138/10 = 13.8

V (X) = ∑(xi^2)/n - Mean of x^2

= 2090/10 - 13.8^2

= 209 - 190.44

V (X) = 18.56

(c) For population standard deviation:

[tex]SD (X) = \sqrt{VAR(X)}[/tex]

SD(X) = [tex]\sqrt{18.56}[/tex]

SD(X) = 4.30

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Step-by-step explanation:

The range from the given table is 9, the population variance is 18.56, and the population standard deviation is 4.30.

Given the value:

xi 10 20 11 17 15 8 7 16 19 15 Total = 138

xi^2 100 400 121 289 225 64 49 256 361 225 Total = 2090

From the above, we get

n =10, ∑xi = 138, ∑xi^2 = 2090

(a) For the range:

Here, the smallest value = 10, and largest value = 19

Therefore, Range = Largest value - Smallest value

Range = 19 - 10 = 9

(b) For population variance:

For mean:

Mean of x = ∑xi/n = 138/10 = 13.8

V (X) = ∑(xi^2)/n - Mean of x^2

= 2090/10 - 13.8^2

= 209 - 190.44

V (X) = 18.56

(c) For population standard deviation:

SD (X) = \sqrt{VAR(X)}SD(X)=

VAR(X)

SD(X) = \sqrt{18.56}

18.56

SD(X) = 4.30

Barry's semester grade point average (GPA). Round to the nearest hundredth is 2.67

The GPA is calculated by following the procedures

the multiplication

credit hour * grade

= 4 * 3 = 12

= 2 * 4 = 8

= 3 * 2 = 6

= 3 * 2 = 6

sum of the products = 12 + 8 + 6 + 6 = 32

sum of credit hour =  4 + 2 + 3 + 3 = 12

The GPA

= sum of the products / sum of credit hour

= 32 / 12 =  2.67

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Answer:

29+8x

Step-by-step explanation:

5+8(3+x)

5+24+8x - Open parentheses

29+8x - Add like terms

The smaller number from the given situation is 16.

Given that, the difference between two whole numbers is 6.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the larger number be x and the smaller number be y.

The difference between two whole numbers is 6.

So, x-y=6

x=6+y --------(I)

Twice the smaller number is 10 more than the larger number.

x+10=2y

x=2y-10 --------(II)

Substitute equation (I) in equation (II), we get

6+y=2y-10

⇒ y=16

Hence, the smaller number from the given situation is 16.

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The maximum height of 32 feet is reached after 1.25 second of flight by the rocket

The function is given as

h(t) = -16t² + 40t + 7

Differentiate the function and set it to 0

-32t + 40 = 0

Add 32t to both sides

32t = 40

Divide both sides by 32

t = 1.25

Hence, the time is 1.25 seconds

In part (a) of this solution, we have

t = 1.25

Recall that

h(t) = -16t² + 40t + 7

So, we have

h(1.25) = -16(1.25)² + 40(1.25) + 7

This gives

h(1.25) = 32

Hence, the maximum height is 32 feet

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Equation of the line which is passing through the point (-2, -6) and has the gradient of -3 is equal to y = -3x -12.

As given in the question,

Gradient of the required equation of the line is given by :

Gradient is slope.

Let slope is represented by m = -3

Line passing through the point (-2, -6) is given by :

( x₁ , y₁) = ( -2 , -6)

Equation of the line which is passing through the point (-2, -6) and has the gradient of -3 is given by :

y - y₁ = m ( x - x₁)

⇒ y - (-6) = (-3)(x - (-2))

⇒ y + 6 = -3( x + 2)

⇒ y + 6 = -3x - 6

⇒ y = -3x -12

Therefore, equation of the line which is passing through the point (-2, -6) and has the gradient of -3 is equal to y = -3x -12.

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The comparison of the equations are

From the question, we have the following equation that can be used in our computation:

-x + 4y = 32

Add x to both sides of the equation

So, we have the following representation

4y = x + 32

Divide through by 4

So, we have

y = 1/4x + 32/4

Evaluate

y = 1/4x + 8

A linear equation is represented as

y = mx + c

Where

Slope = m

As a general rule, linear equations that have the same slope are parallel

This means that the equation y = 1/4x + 1 is parallel to y = 1/4x + 8

Also;

The slopes of perpendicular lines are opposite reciprocals

This means that the equation 4x + y = -3 is perpendicular to y = 1/4x + 8

Lastly, the third equation would neither parallel not perpendicular to the line.

This is because the first equation is parallel and the second equation is perpendicular

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Answer: 24% out of 53 people

Step-by-step explanation:

Answer:

45.3% are men

Step-by-step explanation:

The equivalent expression of 6⁵ is 6² × 6³.

The equivalent expression of 5⁻² × 5⁵ × 5  is 5⁴.

Two algebraic expressions are said to be equivalent if their values obtained by substituting the values of the variables are same.

Equivalent expressions are expressions that work the same even though they look different.

Therefore, let's find the expression, equivalent to 6⁵,

Using law of indices,

[tex]A^{x} X A^{y} = A^{x +y }[/tex]

Hence,

6² × 6³ = 6²⁺³ = 6⁵

5⁻² × 5⁵ × 5 = 5⁻²⁺⁵⁺¹ = 5⁴

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The length of BD is 6.

Given, a right triangle ABC with an altitude BD.

On using concept of Similarity in triangle ADB and CDB,

AD/BD = BD/CD

9/BD = BD/4

36 = BD²

BD² = 36

BD = 6

So, the length of BD is 6.

Hence, the length of BD is 6.

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Answer:

below

Step-by-step explanation:

$ 5.25 /hr * 32.5 hr   *  .77 =  131.38 dollars

to get the slope of any straight line, we simply need two points off of it, wait a minute!!!! holy smokes!! the graph already has two points for us, yeahhh, let's use those then

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-7}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{5}}} \implies \cfrac{ -7 }{ -5 } \implies {\Large \begin{array}{llll} \cfrac{7 }{ 5 } \end{array}}[/tex]

Answer:

Im pretty sure its 12,800 bacteria

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf b = 28}[/tex]

Step-by-step explanation:

Point (x,y) = (2,20)

So, x = 2 and y = 20

Also,

Slope = m = -4

Where b is y-intercept.

Put the above given data in this equation.

20 = (-4)(2) + b

20 = -8 + b

Add 8 to both sides

20 + 8 = b

28 = b

[tex]\rule[225]{225}{2}[/tex]

y=mx+c. y=20

x=2

m=-4

20= -4(2)+c

20= -8+c

20+8=c

28=c

Answer:

.5 feet away

Step-by-step explanation:

3 divided in half is 1.5

so 2 in  half is .5

hope this helps!

Answer:

3.3

Step-by-step explanation:

Plato(edmentum) users

Answer: Troy

Step-by-step explanation:

Troy’s equation has a slope of 28, so next you need to calculate Lucy’s slope:   Go up 25, over to the right 1, so the slope is 25.

Troy has a greater slope, so his is steeper.

The total mixture to contain 8% vinegar so: .06F plus .11S equal to .08(320).Now, we can solve the system of equations using substitution.F + S is 310

.06F + .11S = .08(310)

F = 310 - S      [solve 1st equation for F]

.06(310 - S) + .11S = .08(320)     [substitute into 2nd equation]

18.6 -.06S +.11S = 24.8

.05S = 6.2

S = 124

F + 124 = 310  

F = 186

make a 320mL mixture that contains 8% vinegar, use 186mL of the first brand and 124mL of the second brand.

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The x-intercepts 0 and 30 indicate it takes 30 seconds to return to the surface of the water

The vertex (15, -5) indicates the scuba diver descends for 15 seconds to a depth of 5 meters under the surface before ascending

The equation of the function is given as

d(x) = 1/3|x - 15| - 5

Set d(x) to 0, to determine the x-intercept

So, we have

1/3|x - 15| - 5 = 0

This gives

1/3|x - 15| = 5

So, we have

|x - 15| = 15

Remove the absolute brackets

x - 15 = 15 and x - 15 = -15

Evaluate the equations

x = 30 and x = 0

This means that the diver is at the surface at 0 and 30 seconds

An absolute value function represented as f(x) = a|x - h|  + k has a vertex of (h, k)

This means that

(h, k) = (15, -5)

It means that the diver dived for 15 seconds to get to 5 meters below the water surface

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If Peter were to put one fourth of what he got in his birthday to the bank then peter is putting 10 in the bank

Information given in the problem

Peter got 40 for his birthday

one-fourth of it into his bank to save

The problem requires multiplication of fractions

one fourth means 1 / 4

one fourth of what Peter got is 1/4 * 40

this is calculated as follows

= 1/4 * 40

= 10

Therefore peter have to put 10 into the bank

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The single logarithms found by logarithm properties are listed below:

Case 31

㏒₃ 277809109776

Case 32

㏒₅ 134456

Case 33

5 · ㏒₇ (a / b²)

Case 34

㏑ (a⁶ / b)⁶

Case 35

㏒₇ (c⁴ · [tex]\sqrt[3]{a}[/tex])

Case 36

㏒₈ [w · (√u · v)]

In this problem we find six cases of logarithmic expressions that must be simplified into a single logarithm by logarithm properties. The complete procedure for each case is shown below:

Case 31

8 · ㏒₃ 11 + 4 · ㏒₃ 6

㏒₃ 11⁸ + ㏒₃ 6⁴

㏒₃ (11⁸ · 6⁴)

㏒₃ 277809109776

Case 32

5 · ㏒₅ 7 + 3 · ㏒₅ 2

㏒₅ 7⁵ + ㏒₅ 2³

㏒₅ (7⁵ · 2³)

㏒₅ 134456

Case 33

5 · ㏒₇ a - 10 · ㏒₇ b

㏒₇ a⁵ - ㏒₇ b¹⁰

㏒₇ (a⁵ / b¹⁰)

㏒₇ (a / b²)⁵

5 · ㏒₇ (a / b²)

Case 34

36 · ㏑ a - 6 · ㏑ b

㏑ a³⁶ - ㏑ b⁶

㏑ (a³⁶ / b⁶)

㏑ (a⁶ / b)⁶

Case 35

4 · ㏒₇ c + (1 / 3) · ㏒₇ a

㏒₇ c⁴ + ㏒₇ [tex]\sqrt[3]{a}[/tex]

㏒₇ (c⁴ · [tex]\sqrt[3]{a}[/tex])

Case 36

㏒₈ w + (1 / 2) · ㏒₈ u + (1 / 2) · ㏒₈ v

㏒₈ w + ㏒₈ √u + ㏒₈ √v

㏒₈ [w · (√u · v)]

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The amount of grapes Carmen purchase than Hunter is 3/4 lbs

From the question, we have the following parameters that can be used in our computation:

Carmen = 11/12 lbs

Hunter = 2/12 lbs

The difference between these parameters is the amount of grapes Carmen purchase than Hunter

This is represented as

Difference = Carmen - Hunter

Substitute the known values in the above equation, so, we have the following representation

Difference = 11/12 - 2/12

Evaluate

Difference = 9/12 = 3/4

Hence, the amount of grapes is 3/4 lbs

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