Caleb is 4 times Jessica's age Jessica is twice Noah's age Noah is one year older than Mary Mary is 3 yrs old how old is Caleb

Look at the picture.

The triangles ABC and DEC are similar. Therefore the sides are in proportion:

[tex]\dfrac{AC}{DC}=\dfrac{AB}{DE}[/tex]

AC = 4cm + 16cm = 20cm

DC = 16cm

AB = 15cm

DE = r

Substitute:

[tex]\dfrac{20}{16}=\dfrac{15}{r}\to\dfrac{5}{4}=\dfrac{15}{r}[/tex]      cross multiply

[tex]5r=(4)(15)[/tex]

[tex]5r=60[/tex]     divide both sides by 5

[tex]r=12\ cm[/tex]

The volume of a larger cone:

[tex]V_l=\dfrac{1}{3}\pi\cdot15^2\cdot20=\dfrac{1}{\not3_1}\pi\cdot15\!\!\!\!\diagup^5\cdot15\cdot20=1500\pi\ cm^3[/tex]

The volume of a smaller cone:

[tex]V_s=\dfrac{1}{3}\pi\cdot12^2\cdot16=\dfrac{1}{\not3_1}\pi\cdot12\!\!\!\!\!\diagup^4\cdot12\cdot16=768\pi\ cm^3[/tex]

The volume of the frustum:

[tex]V=V_l-V_s\to V=1500\pi-768\pi732\pi\ cm^3[/tex]

Final answer:

Tonya ran the race approximately 6.13 seconds faster than Jada.

Explanation:

To find out how much faster Tonya ran the race, we need to calculate the difference between their race times.

Tonya's race time is 69.07 seconds, while Jada's race time is 75.2 seconds.

To calculate the difference, we subtract Jada's race time from Tonya's race time: 69.07 - 75.2 = -6.13 seconds.

Therefore, Tonya ran the race approximately 6.13 seconds faster than Jada.

Answer:

407.22 foot is the boat from the base of the lighthouse

Step-by-step explanation:

Given the statement: An observer on top of a 50-foot tall lighthouse sees a boat at a 7° angle of depression.

Let x foot be the distance of the object(boat) from the base of the lighthouse

Angle of depression = [tex]7^{\circ}[/tex]

[tex]\angle CAB = \angle DCA = 7^{\circ}[/tex]       [Alternate angle]

In triangle CAB:

To find AB = x foot.

Using tangent ratio:

[tex]\tan (\theta) = \frac{Opposite side}{Adjacent Base}[/tex]

[tex]\tan (\angle CAB) = \frac{BC}{AB}[/tex]

Here, BC = 50 foot and [tex]\angle CAB =7^{\circ}[/tex]

then;

[tex]\tan (7^{\circ}) = \frac{50}{x}[/tex]

or

[tex]x = \frac{50}{\tan 7^{\circ}}[/tex]

[tex]x = \frac{50}{0.1227845609}[/tex]

Simplify:

AB = x = 407.217321 foot

Therefore, the boat from the base of the light house is, 407.22'

Using the tangent of the angle of depression, the distance from the boat to the base of the lighthouse is calculated to be approximately 407 feet.

To solve this problem, we need to use trigonometry. The angle of depression from the observer at the top of the lighthouse to the boat is the same as the angle of elevation from the boat to the observer because these angles are alternate interior angles formed by parallel lines (the water's surface and the height level at the observer's eyes) and a transversal (the line of sight from the observer to the boat).

We have a right triangle where the lighthouse height is the opposite side to the angle of elevation, and the distance from the boat to the lighthouse is the adjacent side. Using the tangent function, which relates the opposite side to the adjacent side in a right angle triangle, we can set up the following equation:

tangent(7°) = opposite/adjacent or tan(7°) = 50/adjacent

So the adjacent side, which is the distance to the boat, is:

adjacent = 50 / tan(7°)

Using a calculator we find:

adjacent ≈ 50 / 0.1228 ≈ 407.2 feet

Thus, to the nearest foot, the boat is approximately 407 feet away from the base of the lighthouse.

The range is the output, which would be the Y value.

The Y value would be calculated based on the input value for x.

any positive number raised to any value of x would be a positive number so 0.5^x would always be positive.

That would be multiplied by 4, which is a positive value, so the output ( Y value) would always be positive.

The range for this would be (0,∞)

The range of the function f(x) = 4 · 0.5^x is (0, 4], meaning it includes all numbers greater than 0 up to and including 4.

The value of 0.5^x decreases toward zero but never actually reaches it. Because the base is positive, the function will never produce negative values, so the smallest value f(x) can approach is 0. The coefficient 4 simply scales the output, so the function values will range from 0 to some maximum value, which occurs at x = 0. At x = 0, f(x) is at its maximum value, 4 · 1 = 4. Therefore, the range of the function is (0, 4], where 4 is included and 0 is excluded since the function can get arbitrarily close to 0 but never equal it.

Answer:

x = 17.5 and y = 35

Step-by-step explanation:

2x + 10 = y + 10 ( alternate angles )

subtract 10 from both sides

2x = y ⇒ 6x = 3y → (1)

the sum of the 3 angles in the triangle = 180°

6x + y + 10 + 30 = 180 ( replace 6x by 3y )

3y + y + 40 = 180

4y + 40 = 180 ( subtract 40 from both sides )

4y = 140 ( divide both sides by 4 )

y = 35

substitute y = 35 into (1)

2x = 35 ( divide both sides by 2 )

x = 17.5

Answer:

Logically it would be 1/8 chance but since I don't know what color the all are, It's hard to tell

Step-by-step explanation:

Answer:

72 Tiles.

Step-by-step explanation:

Multiply 8 by 9.

8*9=72

Good luck please mark me brainliest

The question is about calculating the area of a rectangle made by square tiles. Jing used a total of 72 tiles by arranging them 8 tiles in length and 9 tiles in width.

This is a problem of area calculation in Mathematics. Jing has to create a rectangle using his square tiles. When it is mentioned that there are 8 tiles along the length and 9 tiles along the width of the rectangle, that means Jing is setting tiles 8 in a row (length) and 9 in a column (width).

The total number of tiles used can be calculated by multiplying the length by the width. This calculation is based on the formula for the area of a rectangle, which is length x width.

So, Jing used 8 tiles (length) x 9 (width) = 72 tiles in total to build the rectangle.

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Product is multiplication.

Since the answer needs to be greater than 2 either the fraction needs to be an improper fraction ( meaning the fraction would be greater than 1) or the whole number would need to be greater than 2.

One answer would be 5 x 2/3 = 3 1/3

The speed of the first car was 6 miles/hour

Acceleration is rate of change of velocity.

[tex]\large {\boxed {a = \frac{v - u}{t} } }[/tex]

[tex]\large {\boxed {d = \frac{v + u}{2}~t } }[/tex]

a = acceleration ( m/s² )

v = final velocity ( m/s )

u = initial velocity ( m/s )

t = time taken ( s )

d = distance ( m )

Let us now tackle the problem!

Given:

Distance between two cars = d = 10 miles

Time Taken = t = 1 hour

Distance covered by the first car = d₁ = 2 + d₂

Unknown:

Speed of the first car = v₁ = ?

Solution:

[tex]d = d_1 + d_2[/tex]

[tex]10 = ( 2 + d_2 ) + d_2[/tex]

[tex]10 = 2 + 2d_2[/tex]

[tex]10 - 2 = 2 d_2[/tex]

[tex]8 = 2 d_2[/tex]

[tex]d_2 = 8 \div 2[/tex]

[tex]d_2 = 4 \texttt{ miles}[/tex]

[tex]\texttt{ }[/tex]

[tex]d_1 = 2 + d_2 = 2 + 4 = 6 \texttt{ miles}[/tex]

[tex]v_1 = d_1 \div t = 6 \div 1 = 6 \texttt{ miles/hour}[/tex]

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle

The speed of the first car is [tex]\boxed{6{\text{ mph}}}[/tex] and the speed of the second car is [tex]\boxed{4{\text{ mph}}}.[/tex]

Further explanation:

The formula of the speed can be expressed as follows,

[tex]\boxed{{\text{Speed}} = \frac{{{\text{Distance}}}}{{{\text{Time}}}}}[/tex]

The formula of the time can be expressed as follows,

[tex]\boxed{{\text{Time}} = \frac{{{\text{Distance}}}}{{{\text{Speed}}}}}[/tex]

Given:

The distance between the two cars is [tex]10{\text{ miles}}.[/tex]

The first car covered 2 miles more than the second car.

Explanation:

Consider the speed of the second car be “[tex]x[/tex]”.

Consider the speed of the first car be “[tex]x+2[/tex]”.

The distance covered by the first car in one hour is [tex]x + 2{\text{ miles}}.[/tex]

The distance covered by the second car in one hour is [tex]x{\text{ miles}}.[/tex]

The total distance covered by two cars is [tex]10{\text{ miles}}.[/tex]

[tex]\begin{aligned}x + 2 + x &= 10\\2x + 2 &= 10\\2x &= 10 - 2\\2x &= 8\\x&= 4\\\end{aligned}[/tex]

The speed of the second car is [tex]4{\text{ miles/h}}.[/tex]

The speed of the first car can be obtained as follows,

[tex]\begin{aligned}{\text{Speed}} &= x + 2\\&= 4 + 2\\&= 6{\text{ miles/h}}\\\end{aligned}[/tex]

The speed of the first car is [tex]\boxed{6{\text{ mph}}}[/tex] and the speed of the second car is [tex]\boxed{4{\text{ mph}}}.[/tex]

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function https://brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Speed and Distance

Keywords: 10 miles, speed of first car, speed of the second car, after one hour, moving toward, each other, 2 miles per hour, one hour.

Answer:

88 square units

Step-by-step explanation:

area= base x height

A=11x8

A=88

Answer:

A

Step-by-step explanation:

The intersection is made when the red and blue line meet. If you make a mark down that looks like 1.5 and if you go up to your y axis the coordinate is 3/4 around the one since it is not over the one.

A. (1.5, 0.75)  coordinate pair is the best estimate of the point of intersection in this graph.

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.

Pair in Order = (x, y)

x is the abscissa, the distance measure of a point from the primary axis x

y is the ordinate, the distance measure of a point from the secondary axis y

By observing the graph the intersection of the two lines is (1.5, 0.75).

As, It lies somewhat in the middle of x = 1 and x = 2, And for y it is more than 0.5 but less than 1 so it must be (1.5, 0.75).

learn more about ordered pairs here :

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Slope-intercept form:

y = mx + b

"m" is the slope, "b" is the y-intercept (the y value when x = 0) or (0,y)

When lines are parallel, their slopes have to be the SAME.

Since the given line's slope is -1/2, the parallel line's slope is also -1/2

y = -1/2x + b

To find "b", plug in the point (2, -2) into the equation

y = -1/2x + b

-2 = -1/2(2) + b

-2 = -1 + b     Add 1 on both sides

-1 = b

y = -1/2x - 1

Answer:

Step-by-step explanation:

How many times must you step back 8 inches after stepping forward 60 inches to end 28 inches from your starting point?

x = number of items that cost $8 per piece

if you buy x of these items for 8 dollars each, then 8*x represents how much you've spent so far. If you start off with $60, then 60-8x = -8x+60 is the total amount of money leftover in your pocket.

If you start off with $60 and end up with $28, then -8x+60 = 28 is the equation that models this. Solving for x leads to finding out how many of these items you have purchased. In this case, the solution is x = 5.

Answer:

2. 31/6  3. -12/1   4. integer  5. rational number

Step-by-step explanation:

2. You multiply the 5 by 6/6, so it becomes 30/6, then add the 1/6. getting you the 31/6.

3. Since -12 is already an integer with no mixed part, you just put it over 1.

4. -12 is an integer, but is not a whole number because it is negative.

5. fractions are rational numbers

Answer: 4. is not a rational nmber. You can't multiply a number that will give you 12. 12 has a integer by it, so that means -12 is a integer. 5. is a rational number.

Step-by-step explanation:

Answer:

Option D is correct.

An equation: h = 28000 -2000m

Step-by-step explanation:

Let h represents the height of the airplane and m represents the minutes.

As per the given statement: An airplane 28,000 feet above ground begins descending at a constant rate of 2,000 feet per minute.

At ground m = 0

h(0) = 28000 feet.

⇒ An airplane descending at a constant rate (r) = - 2000 feet per minute

then,

height(h) of the airplane after m minutes is given by:

h(m) = 28000 - rm ; where r is the rate descending at constant rate and m is the minutes.

Substitute the given values we get;

h(m)= 28000 -2000m

Therefore, an equation which gives the height, h of the airplane after m minutes is; h = 28000 -2000m

Answer:

It IS D) h = 28,000 − 2,000m!

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

67 plus 38 equals 105. the opposite interior equals the outside.

Answer:

So, total gallons were made in all =9.31 gallons

Step-by-step explanation:

We are given

A scientist repeated an experiment three times, making 1.42, 3.81, and 4.08 gallons of a new product

so,

first experiment =1.42 gallons

Second experiment =3.81 gallons

Third experiment =4.08 gallons

now, we can find total gallons

total gallons = first experiment + second experiment + third experiment

total gallons =1.42 gallons + 3.81 gallons +4.08 gallons

total gallons =9.31 gallons

Answer:

42 digits right of the decimal point.

Step-by-step explanation:

Trailing zeroes are those which we get in decimal representation and after that there comes no digit.

We have been given the expression:

[tex]0.4^{24}\cdot 0.375^{22}[/tex]

We will simplify it to get the result that is the right of the decimal point.

[tex]1.19709242282867431640625\cdot 10^{-19}[/tex]

When we will operate [tex]10^{-19}[/tex] that means decimal point will be shifted 19 digits left of its present position.

Hence, we get:

[tex].000000000000000000119709242282867431640625[/tex]

Hence, 42 digits right of the decimal point.

Answer:

42

Step-by-step explanation:

Answer:

10 tacos costs $15.00

Step-by-step explanation:

I like to use ratio's to solve this  type of problem.  I will put cost over number of tacos.

$6.00       x dollars

--------   =  --------------

4 tacos     10 tacos

Using cross products

6 * 10 = 4 * x

60 = 4x

Divide each side by 4

60/4 = 4x/4

15 =x

10 tacos costs $15.00

Answer:

B) $15.00

Step-by-step explanation:

well if 4 taco = $6 just divid to see how mutch one taco is

6.00 divided by 4 = $1.50

now just times 1.50 by 10 to get $15

hope this helped

Answer:

As a number, there is no "number" for the slope of the vertical line (N/A)

Step-by-step explanation:

Remember that slope is the "y" measurements. If there is " ' infinite ' " y's, then there is no exact slope measurement, which makes it N/A

~

The slope of a vertical line is undefined because it does not have a definitive rise over run, as the change in x is zero, leading to division by zero. Graphically, slopes indicate the steepness of a line, with positive slopes inclining upward, negative slopes declining downward, and the slope of a horizontal line being zero. Vertical lines have an infinite slope, which is another way of saying they have no defined steepness in the typical sense.

The slope of a vertical line is a concept that often confuses students, primarily because a vertical line does not have a slope in the way we usually understand it. The slope value of a line typically tells us how much the y-value goes up or down for a unit change along the x-axis. For a horizontal line, the slope equals zero, but a vertical line is different. Since the x-value does not change as the y-value increases or decreases, you would be dividing by zero, which is mathematically undefined. Thus, the slope of a vertical line is undefined.

Graphically, if the slope of a line increases, it becomes steeper, and conversely, if it decreases, the line becomes flatter. A positive slope means that as you move to the right along the x-axis, the line goes up. On the other hand, a negative slope indicates that the line goes down as you move right. However, these concepts do not apply to vertical lines, as they do not have a slope that could be described as positive or negative. Instead, their infinite slope is a way of expressing that they are not functionally graded.

Answer: 1,596 cubic cm. To find the volume, you need to multiply all the three sides given.

Step-by-step explanation:

12cm * 7 cm* 19cm = 1596 cm^3

The volume of the box given the length, width and height is 1,596 cm³

Given:

Length of the box = 12cm

Width of the box = 7 cm

Height of the box = 19 cm

Volume of the box = length × height × width

= 12 cm × 7 cm × 19 cm

= 1596 cm³

Therefore, the volume of the box is 1,596 cm³

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Answer:

$590.50

Step-by-step explanation:

Juan earns $310 every week.

He earns 5.5% on merchandise sold.

On a week he sells $5100, we need to figure 5.5% of that amount and then add $310.

$5100

X  .055

______

$280.50 commission.

+ 310.00 salary for the week

_______

$590.50

Answer:

(A)

[tex]x=-4[/tex]

(B)

[tex]g(x)=\frac{3x-1}{x+4}+4[/tex]

(C)

[tex]x=-17[/tex]

Step-by-step explanation:

we are given

[tex]f(x)=\frac{3x-1}{x+4}[/tex]

(a)

we know that

any function is undefined when denominator =0

so, we can set denominator =0

and then we can solve for x

[tex]x+4=0[/tex]

[tex]x=-4[/tex]

So, it does not have solution at [tex]x=-4[/tex]

(b)

If g(x) is a vertical shift up 4 units from f(x)

Whenever we shift vertically upward by 'a' units , we always add 'a' to y-value

so, we get

g(x)=f(x)+4

we get

[tex]g(x)=\frac{3x-1}{x+4}+4[/tex]

Graph:

(C)

we can set g(x)=8

and then we can solve for x

[tex]8=\frac{3x-1}{x+4}+4[/tex]

[tex]8\left(x+4\right)=3x-1+4\left(x+4\right)[/tex]

[tex]8x+32=7x+15[/tex]

[tex]x=-17[/tex]

Okay, notice one thing right off the bat? 60 degrees on a right triangle (unit circle w/ terminal arm) will create the infamous 30-60-90 triangle.

We can use this to our advantage. Since sin is the y-coordinate on the unit circle. We need to solve for the longest side of a 30-60-90 triangle.

We find that the long side (y) of our 30-60-90 triangle is sqrt(3)/2. Since this is in quadrant 1, we know it is positive.

So -- sin60° = sqrt(3)/2

The value of the sine of the angle 60 degrees will be √(3) / 2.

A right triangle's ratio of the hypotenuse's length to the length of the side opposite an angle is represented by the sine function, a trigonometric function. We can calculate the sine function for a generally understood angle of 60 degrees.

Consider an equilateral triangle with all sides equal for a 60-degree angle. The triangle's side across from the 60-degree angle is equal in length to the other sides.

The ratio of the length of the side opposite the 60-degree angle to the length of the hypotenuse is √(3 / 4) because an equilateral triangle has all angles measuring 60 degrees.

Sin 60 degrees hence equals 1/2.

The sine of 60 degrees is, therefore, √(3 / 4) or √(3) / 2.

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The sale price as a function of the original selling price can be represented by the equation: Sale price = Original selling price - (40% of Original selling price). The inverse function represents the original selling price when the sale price is given. It allows us to find the price at which the furniture was originally sold before the discount was applied.

a) The sale price as a function of the original selling price can be represented by the equation:

Sale price = Original selling price - (40% of Original selling price)

For example, if the original selling price is $100, the sale price would be:

Sale price = $100 - (40% of $100) = $100 - $40 = $60.

b) To find the inverse of this function, we can swap the dependent and independent variables. Let's call the original selling price 'x' and the sale price 'y'. So, the inverse function is given by:

Original selling price = Sale price + (40% of Sale price)

c) The inverse function represents the original selling price when the sale price is given. It allows us to find the price at which the furniture was originally sold before the discount was applied.

Answer:

The answer should be the second option or 10 cm.

The only thing is that PQ is just a little longer than RS and PQ is 10 cm but A. 15 cm is to long, C. 20 cm is also to long and D. 5 cm is to short.

So i belive it is B. 10 cm.

Hope this helped, can i have brainliest?

Answer:

37

Step-by-step explanation:

Let the answer be represented by xy  where x is the tens digit and y is the ones digit.

The ones digit of a two-digit number is 4 more than the tens digit.

y = x+4

the sum of that number and the number reversed is 110

xy+yx = 110

Lets rewrite this vertically

 x y

 y x

------

1 1 0

We can replace y with x + 4  I will put the 4's in a separate row up top for ease of writing

 4 4

 x x

 x x

------

1 1 0

Taking the one's column, we get

2x +4 = 0  and I will assume there is a carry of 10

so rewriting

2x+4 = 10

Subtract 4 from each side

2x+4 -4 = 10-4

2x =6

Divide each side by 2

2x/2 = 6/2

x=3

We still need to find y

y = x+4

Substituting in x

y = 3+7

y =7

The number is xy

37

Answer:

Step-by-step explanation:

ohhhhhh

[tex]\text{Use}\ (a+b)^2=a^2+2ab+b^2\\\\x^2+4x+4=25\\\\x^2+2(2)(x)+2^2=25\\\\(x+2)^2=25\iff x+2=\pm\sqrt{25}\\\\x+2=-5\ \vee\ x+2=5\qquad\text{subtract 2 from both sides}\\\\\boxed{x=-7\ \vee\ x=3}[/tex]

Other method:

[tex]x^2+4x+4=25\qquad\text{subtracr 25 from both sides}\\\\x^2+4x-21=0\\\\x^2+7x-3x-21=0\\\\x(x+7)-3(x+7)=0\\\\(x+7)(x-3)=0\iff x+7=0\ \vee\ x-3=0\\\\x+7=0\qquad\text{subtract 7 from both sides}\\\boxed{x=-7}\\\\x-3=0\qquad\text{add 3 to both sides}\\\boxed{x=3}[/tex]

Subtract the cost of the soda from the total price to find how much all the pizza cost. Then divide the total cost of the pizza by the number of slices bought:

7 -1 = 6

Total cost of pizza was $6

6 / 4 = 1.50

Cost for one slice of pizza $1.50

Answer:

24.25

Step-by-step explanation:

8*x=194

8/8 crosses out and 194/8=24.25

with means x=24.25