PICK ONE !!!!!!!!!!!!!

Answer:

50

Step-by-step explanation:

2(Mr stack's speed) = Coach Pugh's speed - 5mph

Mr stack's speed = (105mph - 5mph)/2

Mr stack's speed = 100mph/2

Mr stack's speed = 50mph

Answer:  C) y = -3x + 1

Step-by-step explanation:

     x          y  

   -2          7

    2         -5

    4         -11

    6         -17

    10       -29

Choose any two coordinates to find the slope: \(m=\dfrac{y_2-y_1}{x_2-x_1}\)

m = -6/2

   = -3

Choose any point and plug it into the Point-Slope formula:  \(y-y_1=m(x-x_1)\)  

y - 7 = -3(x  + 2)

y - 7 = -3x - 6

y      = -3x + 1

The probability of drawing a jack, given that we are told it is a face card, is 1/3 or approximately 0.33.There are 12 face cards in a well-shuffled euchre deck, comprising of 4 jacks, 4 queens, and 4 kings. The probability of drawing a face card from the deck is 12/32, or 3/8.

Now, we are asked to find the probability of drawing a jack, given that we already know the card is a face card. This can be calculated using conditional probability, which is the probability of an event occurring given that another event has already occurred.

The probability of drawing a jack given that the card is a face card can be represented as P(Jack | Face card). Using Bayes' theorem, we can calculate this probability as follows:

P(Jack | Face card) = P(Face card | Jack) * P(Jack) / P(Face card)

Here, P(Face card | Jack) represents the probability of drawing a face card given that the card is a jack, which is 1. P(Jack) represents the probability of drawing a jack from the deck, which is 4/32 or 1/8.

We already know that P(Face card) is 3/8.Substituting these values into the formula, we get:

P(Jack | Face card) = (1 * 1/8) / (3/8) = 1/3.

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Answer:

V = 5024 ft³

Step-by-step explanation:

the volume (V) of a cylinder is calculated as

V = πr²h ( r is the radius and h the height )

since diameter = 20, then r = 20 ÷ 2 = 10

V = 3.14 × 10² × 16

  = 3.14 × 100 × 16

  = 314 × 16

  = 5024 ft³

Answer:

v = 5024

Step-by-step explanation:

The formula used to find the volume (v) of a cylinder is \(v = \pi r^2h\), where r = radius and h = height. Here, we are using 3.14 instead of pi.

We are given a height of 16 ft, and a diameter of 20 ft. The radius is simply half of the diameter, so our radius is 10 ft. Put these two values into the formula and solve.

\(v = 3.14*10^2*16\)

If you were to be using pi, your answer exactly  would be v = 5026.55. Using 3.14, it is v = 5024.

So, Tracy paid $12.50 for the encyclopedia and $45.50 for the math book.

In mathematics, an equation is a statement that shows the equality between two expressions. The expressions can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. An equation usually has an equals sign (=) between the two expressions. The equals sign indicates that the two expressions have the same value.

Here,

Let's use variables to represent the prices of the math book and the encyclopedia.

Let x be the price of the encyclopedia.

According to the problem, the price of the math book is 8 dollars more than 3 times the price of the encyclopedia. So, the price of the math book can be represented as:

=3x + 8

The total cost of the two books is given as 58 dollars. Therefore, we can write the equation:

x + (3x + 8) = 58

Simplifying and solving for x, we get:

4x + 8 = 58

4x = 50

x = 12.50

So, the price of the encyclopedia is $12.50.

To find the price of the math book, we can substitute x = 12.50 into the expression we derived earlier:

=3x + 8

= 3(12.50) + 8

= 37.50 + 8

= 45.50

Therefore, the price of the math book is $45.50.

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Answer:

-3x^2-4x-43

Step-by-step explanation:

factor out the negative signs

remove parenthesis

The age of Barbra is 22 years.

The algebraic method for solving simultaneous linear equations is the substitution method. A quantity of one variable through one expression is replaced in the second equation, as the name implies.

Now, according to the question.

Let 'a' be the age of Alice.

Let 'b' be the age of Barbra

Let 'c' be the age of Carol.

The sum of age of all three sisters is 68 years.

Thus,  a + b + c = 68

Now, as Alice is three years younger than Barbra.

a = b - 3

and, Barbra is 5 years younger than Carol.

b = c - 5

c = b + 5

By substitution of values of a and c in total age.

(b - 3) + b + (b + 5) = 68

3b - 3 + 5 = 68

On solving the expression.

b = 22

Therefore, the age of Barbra is 22 years.

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Answer:

Kathy and Lilly

Step-by-step explanation:

Because they both are nearest to the leader distance of 5 meters

Answer:

(c) Paul's model predicts a score of 51 for 3 hours

(d) 30 represents the y intercept

Step-by-step explanation:

Given

\(y = 7x + 30\)

Solving (c): What is y when x is 3

Substitute 3 for x in \(y = 7x + 30\)

\(y = 7*3 + 30\)

\(y = 21 + 30\)

\(y = 51\)

Solving (d): What does 30 represent

An equation is represented as:

\(y = mx + b\)

Where

\(b = y\ intercept\)

Compare: \(y = mx + b\) to \(y = 7x + 30\)

\(b = 30\)

This implies that 30 represents the y intercept

Answer:

16x+6

Step-by-step explanation:

5x+2+3x+1+5x+2+3x+1 =

16x+6

Answer:

16x + 2

Step-by-step explanation:

\(\boxed{\begin{minipage}{4 cm}\underline{Perimeter of a rectangle}\\\\$P=2(w+l)$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width. \\\phantom{ww}$\bullet$ $l$ is the length.\\\end{minipage}}\)

Given expressions:

To write an expression for the perimeter of the rectangle, substitute the given expressions for the width and length into the perimeter formula:

\(\begin{aligned}\implies \textsf{Perimeter} &=2\left(5x+2+3x-1 \right)\\ &= 2(5x+3x+2-1)\\&=2(8x+1)\\&=16x+2\end{aligned}\)

Answer:

1. $145

2. 45+25x=total $

Step-by-step explanation:

45+(25•4)=145

Step-by-step explanation:

Given:

10 GB included with plan

$45 per month

$25 per GB over the amount of 10

Need to find out:

How much would Kadeesha have to pay in a month where she used 4 GB over the limit, how much would it be if it went over xx GB?

Let's solve the first problem:

10 GB included + 4 GB (over) =14 total GB

$45=10GB. $25×4= 4 GB over.

$45+$100=$145

Therefore, Kadeesha would have to pay $145 if she went 4 GB over the 10.

Now, let's solve the next problem:

So, for this problem we are going to find the amount it wil be in other various amounts. To do this we will create a chart /table

$45 ------> 10GB

$70 -----> 11 GB

$95 ----> 12 GB

$120 ---> 13 GB

$145 ---> 14 GB

$170 ---> 15 GB

and so on....

but here we can see any given amount will be her usual Phone bill amount ($45), with the 10 GB and an additional $25 for every added GB.

if something is unclear, or seems wrong just let me know!

I hope this helps:)

Answer:

It might be weird but i is the answer and I don't know why exactly.

Step-by-step explanation:

I think it's because there is no real number when having a negative square.

The dependent variable is the "height the ball bounces". The dependent variable is an essential component of the scientific experiment. It is the variable that you control to determine how the changes will impact the subject being investigated.

Height the ball bounces is your dependent variable, which varies based on the other variables.The term dependent variable refers to a variable whose value is determined by the presence of one or more variables (i.e., the independent variables) being evaluated. The dependent variable is commonly represented on the vertical or y-axis of a graph, while the independent variable is frequently shown on the horizontal or x-axis of the same graph.

The term dependent variable refers to a variable whose value is determined by the presence of one or more variables (i.e., the independent variables) being evaluated. The dependent variable is commonly represented on the vertical or y-axis of a graph, while the independent variable is frequently shown on the horizontal or x-axis of the same graph. The dependent variable is the "height the ball bounces". The dependent variable is an essential component of the scientific experiment.

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The simplified form of the expression is \(\(3\)\) after using trigonometric identities and canceling out terms. The original expression, \(\(2\sin^2 x + 2\cos^2 x + \frac{\tan x \cos x}{\sin x}\),\) simplifies to \(\(3\).\)

To simplify the expression \(\(2\sin^2 x + 2\cos^2 x + \frac{\tan x \cos x}{\sin x}\),\) we can use trigonometric identities to rewrite the terms in a simplified form. Let's break it down step by step:

Step 1: Simplify the terms involving sine and cosine:

Using the identity \(\(\sin^2 x + \cos^2 x = 1\),\) we can simplify \(\(2\sin^2 x + 2\cos^2 x\) to \(2(1)\),\) which is simply \(\(2\).\)

Step 2: Simplify the term involving tangent:

Recall that \(\(\tan x = \frac{\sin x}{\cos x}\).\) By substituting this into the expression, we get \(\(\frac{\frac{\sin x}{\cos x} \cdot \cos x}{\sin x}\).\) The \(\(\cos x\)\) terms cancel out, leaving us with \(\(\frac{\sin x}{\sin x}\),\) which simplifies to 1.

Step 3: Combine the simplified terms:

Now that we have simplified \(\(2\sin^2 x + 2\cos^2 x\) to \(2\)\) and \(\(\frac{\tan x \cos x}{\sin x}\) to \(1\),\) we can combine the terms. The expression becomes \(\(2 + 1\),\) which further simplifies to \(\(3\).\)

Therefore, the simplified form of \(\(2\sin^2 x + 2\cos^2 x + \frac{\tan x \cos x}{\sin x}\) is \(3\).\)

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A graph that would display the narrowest parabola is f(x) = -4x² - 30x.

In Mathematics, the standard equation of the directrix lines for any parabola can be modeled or represented by the following mathematical expression:

y = a(x - h)² + k.

Where:

Generally speaking, the larger the absolute value of the leading coefficient of a quadratic function, the narrower would be graph of its parabola.

In this context, we have the following:

y = -2x²+x+3; a = -2

f(x) = -4x² - 30x; a = -4

|a| = |-2| = 2

|a| = |-4| = 4

Therefore, |-2| is less than |-4|.

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Answer:

Let's say the number of sweets that Amol has is A.

According to the problem, the number of sweets that Gemma has is 6 times the number of sweets that Amol has. Therefore, Gemma has 6A sweets.

The number of sweets that Harry has is half the number of sweets that Gemma has. Therefore, Harry has 1/2 * 6A = 3A sweets.

So the ratio of the number of sweets that Amol, Gemma, and Harry have respectively is:

A : 6A : 3A

Simplifying this ratio by dividing each term by A, we get:

1 : 6 : 3

Therefore, the ratio of the number of sweets that Amol has to the number of sweets that Gemma has to the number of sweets that Harry has is 1:6:3

Answer:

-1/3

step-by-step explanation:

-21=-39k+-24

39k = -24 + 21

39k = -3 (divide each side by 39)

k = -1/3

Answer:

The answer would be B < - 1

Answer:

I'ts B, (5,2)

Step-by-step explanation:

It's B :)

Answer:

A

Step-by-step explanation:

the equation is the second one

Answer:

k=10

Step-by-step explanation:

The reason is that we should solve the following equation:

4k+5 + 6k+10 + (180-115) = 180

by doing some basic algebra we get:

10k = 100

thus: k=10

The total fixed costs for the event amount to £2,800, which includes the security costs and the cost of the main band. Fixed costs are expenses that do not change with the number of attendees or sales.

To calculate the total fixed costs for the event, we need to identify the costs that do not change with the number of attendees. Based on the given information, the fixed costs include the security costs and the cost of the main band. Let's break it down:

Security costs: The security costs of £300 are fixed and do not depend on the number of attendees. This means the cost remains the same regardless of how many tickets are sold.

Cost of the main band: The cost of the main band is £2,500. Similar to the security costs, this cost is fixed and does not vary based on the number of attendees.

Therefore, the total fixed costs for the event would be the sum of the security costs and the cost of the main band:

Total Fixed Costs = Security Costs + Cost of Main Band

Total Fixed Costs = £300 + £2,500

Total Fixed Costs = £2,800

However, it's important to note that the cost of the supporting band, ticket prices, and the cost of the water bottles are not fixed costs. The cost of the supporting band and the cost of the water bottles are variable costs as they depend on the number of attendees. The ticket prices represent revenue, not costs.

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Here is hοw far away frοm the cliff's edge Andrea is 233 feet.

The British imperial and American custοmary systems οf measurement bοth use the unit οf length knοwn as the fοοt (plural: feet), standard symbοl: ft. Usually used as an alternate symbοl is the prime symbοl, ′. One yard is equal tο three feet in bοth custοmary and imperial measures; οne fοοt is equal tο 12 inches.

Thrοughοut histοry, the "fοοt" was a cοmpοnent οf a number οf regiοnal systems οf measurement, including the Greek, Rοman, Chinese, French, and English systems. Frοm οne natiοn tο the next, frοm οne city tο the next, and perhaps frοm οne trade tο the next, it varied in length. Its length was οften divided intο 12 inches οr 16 numbers and ranged frοm 250 tο 335 mm in length, thοugh this was nοt always the case.

42º is the base angle.

The grοund distance is οn the next side.

The height οf the οther side is 215 - 5.25= 209.75.

As a result, the distance is calculated as fοllοws:

tan(42º) = 209.75/d

d = 209.75/tan(42º)

d = 233 ft.

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The theoretical probability of rolling a one or two is 3/5 or 0.6 as a decimal.

The theoretical probability of an event happening is the number of favorable outcomes divided by the total number of possible outcomes.

In this case, Alexandria rolled the number cube 60 times and recorded her results in the table.

Looking at the table, we can see that the number 1 came up 16 times and the number 2 came up 20 times.

So the number of favorable outcomes is 16 + 20 = 36.

And the total number of possible outcomes is 60.

Therefore, the theoretical probability of rolling a one or two is:

P(1 or 2) = favorable outcomes/total outcomes = 36/60

Simplifying the fraction, we get:

P(1 or 2) = 3/5

So the theoretical probability of rolling a one or two is 3/5 or 0.6 as a decimal.

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Answer:

3rd Option    -     3(x-4) = 6x

Step-by-step explanation:

To remove the fractions we escalate them up to the other side. So to remove the x under 3 we do the following :

\(\frac{3}{x} = \frac{6}{x-4}\)   ----->  \({3}= \frac{6x}{x-4}\) (As you can see the x now goes to the numerator of the right side)

Now to remove x-4 under 6x we do the following :

\({3}= \frac{6x}{x-4}\)   ------> \(3(x-4)= {6x\)

Therefore giving our answer as the 3rd option.

Hope this helped and have a good day

Answer:

Step-by-step explanation:

x^2 + 2x - 59 = 3x - 3

x^2 + 2x - 3x -59 +3 = 0

x^2 - x - 56 = 0

x^2 - (8 - 7)x - 56 = 0

x^2 - 8x + 7x - 56 = 0

x(x - 8) + 7(x - 8) = 0

(x + 7)(x - 8) = 0

either (x + 7) = 0

Or,  (x - 8) = 0

x + 7 = 0

x = 0 - 7

x = -7

x - 8 = 0

x = 0 + 8

x = 8

therefore x = -7 , 8

Answer:

(x - 7)^2 + (y - 2)^2 = 5^2

Step-by-step explanation:

Center at (7, 2); radius 5

Adapt (x - h)^2 + (y - k)^2 = r^2 to this situation.  Replace h by 7, k by 2 and r by 5:

(x - 7)^2 + (y - 2)^2 = 5^2

Answer:

Step-by-step explanation:

The diagonals of a quadrilateral divide it into two congruent triangles. In this case, the diagonals of quadrilateral ABCD with vertices A (-4,9), B (3,9), C(2,3), D(-5,3) are AC and BD.

To find the intersection point of the two diagonals, we can use the equations of the two lines.

The equation of line AC can be represented as y = mx + b, where m is the slope of the line and b is the y-intercept.

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

m = (3-9)/(2-(-4)) = -6/6 = -1

b = y1 - mx1

b = 9 - (-1)(-4) = 9+4 = 13

The equation of the line is y = -x + 13

Similarly, the equation of line BD can be represented as y = nx + c, where n is the slope of the line and c is the y-intercept.

n = (y4-y3)/(x4-x3) = (3-9)/(-5-3) = -6/8 = -3/4

c = y3 - nx3

c = 3 - (-3/4)(-5) = 3 + 15/4 = 27/4

The equation of the line is y = -3/4 x + 27/4

Now we can find the point of intersection (x,y) by solving the following system of equations

-x + 13 = -3/4 x + 27/4

Multiply the equation 1 by 4

-4x + 52 = -3x + 27

Add 3x to both sides

-x + 52 = 27

Subtract 27 from both sides

-x = -25

x = 25

Now we can substitute this value of x in any of the equation to find the value of y

y = -x + 13

y = -25 + 13

y = -12

So, the coordinates of the intersection of the diagonals of quadrilateral ABCD are (25,-12).

Answer:

after 80 years, approximately 2.15 grams of the initial 16 grams of cesium-137 would remain. This means that about 13.4 grams would have decayed during this time period.

Answer:

An arithmetic sequence has a constant difference between each consecutive pair of terms. This is similar to the linear functions that have the form y=mx+b, and geometric sequence has a constant ratio between each pair of consecutive terms. This would create the effect of a constant multiplier.