ΔDEF and ΔXYZ are similar isosceles triangles. What is the measure of X?



75°
105°
60°
30°

Claire will pay $309.01 for the bike.

Answer:

[tex]P(t)=4(1.019)^t[/tex]

Step-by-step explanation:

we know that

The equation of a exponential growth function is equal to

[tex]P=a(1+r)^t[/tex]

where

P ---> is the world's population

t ---> is the number of years since 1945

a ---> is the initial population in 1945

r ---> is the percent rate of growth

we have

[tex]r=1.9\%=1.9/100=0.019[/tex]

substitute

[tex]P=a(1+0.019)^t[/tex]

[tex]P=a(1.019)^t[/tex]

Remember that

There were  approximately 4 billion people in the world in 1975

That means

Since year 1975 the initial value a=4 billion people

substitute

[tex]P(t)=4(1.019)^t[/tex]

Answer:

[tex]\frac{2}{5}[/tex]

Step-by-step explanation:

Note the [tex]\sqrt[3]{8}[/tex] = 2 and [tex]\sqrt[3]{125}[/tex] = 5

Thus

[tex]\sqrt[3]{\frac{8}{125} }[/tex] = [tex]\frac{\sqrt[3]{8} }{\sqrt[3]{125} }[/tex] = [tex]\frac{2}{5}[/tex]

Answer:

2/5

Step-by-step explanation:

8 = 2^3

125 = 5^3

Answer:

Yes, it is.

Step-by-step explanation:

The second 8 in 8.8 is greater than the 0 in 8.01.

What have you done?

Answer:

The numbers are 15 and 6.

Step-by-step explanation:

We can solve the problem algebraically (using equations). First, write equations that represent the situation.

Choose variables to represent the numbers:

let the numbers be "x" and "y"

Take apart each section of the problem and make an equation.

"The sum of two numbers is 21"

x + y = 21             Sum means the answer when you add numbers

"Their difference is 9"

x - y = 9               Difference means the answer when you subtract numbers

Using the two equations, you can solve using elimination. With this method, you get rid of one of the variables, so you can easily solve for the other one. You can use elimination when one of your variables have the same variable number. Both equations have "1x" and "1y" ("1" is never written).

Add the equations together by adding normally, with each of the terms with the same variable.

.     x + y = 21             Add each term

+     x - y = 9            (x + x = 2x)     (y + (-y) = 0)     (21 + 9 = 30)

.   2x + 0 = 30         "y" variable cancelled out

.          2x = 30        

.       2x/2 = 30/2         Divide both sides by "2" to isolate "x"

.            x = 15         Answer for one number

To find the other number, substitute 'x' for 15 into one of the equations.

x + y = 21

15 + y = 21         Isolate "y" now

15 - 15 + y = 21 - 15         Subtract 15 from both sides

y = 21 - 15         15-15 cancelled out on the left side. Solve right side.

y = 6       Answer for second number

Therefore the two numbers are 15 and 6.

Answer:

im stuck on a similar problem right now

Answer:

8.2

Step-by-step explanation:

Use cosine law:

BC² = 7² + 9² - 2(7)(9)cos(60)

BC² = 67

BC = sqrt (67)

BC = 8.1853

BC = 8.2 (nearest tenth)

Answer:

By bike= 4 hours

By walk= 3 hours

Step-by-step explanation:

Given: Sydney travel by bike at 9 mph

           Sydney travel by walk at 7 mph.

           Total trip time= 7 hours

           Distance to bookstore= 57 miles.

Lets assume the time spent travelling by bike be "x".

∴ Time spent travelling by walk is [tex](7-x)[/tex]

Now, lets find the distance travelled on bike and by walk.

we know, [tex]Distance= speed\times time[/tex]

∴ Distance by bike= [tex]9\times x= 9x[/tex]

   Distance by walk= [tex]7\times (7-x)[/tex]

Using distributive property of multiplication.

∴ Distance by walk= [tex]49-7x[/tex]

Next, forming an equation for total distance travelled to find x.

⇒ [tex]9x+ (49-7x)= 57\ miles[/tex]

Opening parenthesis

⇒ [tex]9x+49-7x= 57[/tex]

⇒[tex]2x+49= 57[/tex]

Subtracting both side by 49

⇒[tex]2x= 8[/tex]

dividing both side by 2

⇒[tex]x= \frac{8}{2}[/tex]

∴[tex]x= 4\ hours[/tex]

Hence, time spent travelling on bike is 4 hours.

Subtituting the value x to find the time spent travelling by walk.

Times spent travelling by walk= [tex]7-4= 3\ hours[/tex]

hence, time spent travelling by walk= 3 hours

Answer:

7 : 3

Step-by-step explanation:

Answer:7:3

Step-by-step explanation:

The other colors are just to throw you off,7 yellow to 3 blue is 7:3

Answer:67.2

Step-by-step explanation:

3.5+2.1=5.6

6 times 5.6 is 33.6 then 33.6 times 2 is 67.2

Answer:

x = 6

Step-by-step explanation:

x = 3 is the equation of a vertical line parallel to the y- axis.

The equation of a parallel line will therefore be a vertical line.

The equation of a vertical line is

x = c

where c is the value of the x- coordinates the line passes through.

The line passes through (6, 1) with x- coordinate 6, thus

x = 6 ← equation of parallel line

Final answer:

The equation of the line that is parallel to x = 3 and passes through (6, 1) is x = 6.

Explanation:

The question relates to finding the equation of a line that is parallel to another line, specifically the line x = 3, and that also passes through a given point, namely (6, 1). Since the line x = 3 is a vertical line, any line parallel to it will also be vertical and have an equation of the form x = k, where 'k' is a constant.

In this case, the line we are looking for must go through the point (6, 1), which means it will have the same x-coordinate as this point. Therefore, the equation of the line is simply x = 6.

The total amount that Karen will be for the sweatshirt including tax will be $32.10.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Karen buys a sweatshirt for $30. The sales sold be tax in her state is 7%.

The total amount that Karen will be for the sweatshirt including tax will be calculated as,

Total cost = $30 x (1 + 7%)

Total cost = $30 x (1 + 0.07)

Total cost = $30 x (1.07)

Total cost = $32.10

The total amount that Karen will be for the sweatshirt including tax will be $32.10.

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Answer:

The actual area of the page will be 120 square inches.

Step-by-step explanation:

Janice is creating a page of scrapbook having vertices (2,1), (7,1), (7,7), and (2,7).

If we plot the points on the coordinate plane then we will see that the page is of a rectangular shape with length (7 - 1) = 6 units which is parallel to the y-axis and width (7 - 2) = 5 units which is parallel to the x-axis.

So, the area of the page is (6 × 5) = 30 square units.

Now, given that 1 square unit is equivalent to 4 square inches.

Therefore, the actual area of the page will be (30 × 4) = 120 square inches. (Answer)

Answer:

The costs of the ski packages will be the same if you set them equal to each other. The cost will be the same after 5 hours. The cost will be $35 for both packages.

Step-by-step explanation:

5 + 5x = 20 + 2x                     Set the equations equal

-5            -5                             Subtract 5 from both sides

5x = 15 + 2x

-2x          -2x                           Subtract 2x from both sides

3x = 15                                    Divide both sides by 3

x = 5

Answer:

(3  x 40) - 85

120 - 85

35 video games

Answer:

No, the cone will not hold all of the ice cream.

Step-by-step explanation:

Given:

" According to the Joy Cone Company, their waffle cones have a diameter of 2 5/8 inches and a  height of 6 inches.

If you place one scoops of ice cream (in the shape of a sphere) with a diameter of 2 7/8 inches would let  it melt.

Now, to explain mathematically will the cone hold all of the ice cream.

Taking the value of π = 3.14.

So, to get the volume of waffle cone we put formula:

Height (h) = 6 inches.

Diameter = [tex]2\frac{5}{8}=\frac{21}{8}\ inches.[/tex]

Thus radius (r) = Diameter ÷ 2 = [tex]\frac{\frac{21}{8}}{2} =\frac{21}{16} \ inches.[/tex]

[tex]Volume=\pi r^2\frac{h}{3}[/tex]

[tex]Volume=3.14\times \frac{21}{16} \times \frac{21}{16} \times \frac{6}{3}[/tex]

[tex]Volume=3.14\times 1.31\times 1.31\times 2[/tex]

[tex]Volume=10.78\ inches^3.[/tex]

The volume of waffle cone = 10.78 inches³.

Now, to get the volume of scoop which is in the shape of sphere we put formula:

Diameter = [tex]2\frac{7}{8} =\frac{23}{8} \ inches.[/tex]

Thus radius (r) = Diameter ÷ 2 [tex]=\frac{\frac{23}{8}}{2} =\frac{23}{16} \ inches.[/tex]

[tex]Volume = \frac{4}{3} \pi r^3[/tex]

[tex]Volume = \frac{4}{3} \times 3.14\times \frac{23}{16} \times \frac{23}{16} \times \frac{23}{16}[/tex]

[tex]Volume=1.33\times 3.14\times 1.44\times 1.44\times 1.44[/tex]

[tex]Volume=12.47\ inches^3.[/tex]

The volume of one scoop of ice cream = 12.47 inches³.

So, as the volume of scoop of ice cream is more than the volume of cone.

Thus, if placing one scoop of ice cream in the cone and let it melt, the cone will not hold all of the ice cream.

Therefore, no the cone will not hold all of the ice cream.

The ice cream scoop will not fit into the cone due to volume differences.

The ice cream scoop will not fit into the cone. To determine this mathematically, we need to compare the volume of the cone to the volume of the ice cream scoop.

The volume of the cone can be calculated using the formula for the volume of a cone: V = 1/3 × π × r² × h.

Similarly, the volume of the sphere (ice cream scoop) can be calculated using the formula for the volume of a sphere: V = 4/3 × π × r³.

By plugging in the given measurements, we can determine that the volume of the ice cream scoop will be greater than the volume of the cone, indicating that the ice cream scoop will not fit into the cone.

Answer:

0.6554 is the probability that the mean number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons.                                  

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 4000 gallons

Standard Deviation, σ = 125 gallons

Sample size, n = 40

We are given that the distribution of amount of fuel is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

Central limit theorem:

As the sample size increases, the distribution of sample mean has a similar popular distribution shape.

P(sample of 40 jumbo jets will be less than 3950 gallons)

P(x < 3950)

[tex]P( x < 3950) = P( z < \displaystyle\frac{3950 - 4000}{125}) = P(z < -0.4)[/tex]

Calculation the value from standard normal z table, we have,  

[tex]P(x < 3950) = 0.6554 = 65.54\%[/tex]

0.6554 is the probability that the mean number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons.

The probability that the number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons is 0.66.

it is given that

Mean μ= 4000 gallons

Standard deviation σ = 125 gallons

Number of trials x = 3950 gallons

Z-score = (x-μ)/σ

Z-score = (3950-4000)/125

Z-score = -0.4

So probbaility P(x<3950) = P(z<-0.4)

From the standard normal table,

P(x<3950) = 0.66

Therefore, the probability that the number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons is 0.66.

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Answer:

t=100-2x

Step-by-step explanation:

The amount of water in the cup after t seconds can be represented by the linear function Y = 100 - 2t. This equation is derived from the initial amount of water in the cup and the rate at which water is being poured out.

The function that shows the amount of water in the cup after t seconds is a linear function. It can be represented as Y = 100 - 2t. In this equation, Y represents the amount of water left in the cup and t represents time in seconds.

This equation comes from the initial amount of water (100 milliliters) minus the rate of water being poured out of the cup (2 milliliters per second times the number of seconds). For example, after 3 seconds, the amount of water left would be 100 - 2*3 = 94 milliliters.

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The function h(x) = x^2 - 1 has a negative average rate of change over the interval from x = -∞ to x = 0, which is where the parabola is decreasing toward its vertex at the origin.

The student asked over which interval the function h(x) = x^2 - 1 has a negative average rate of change. The average rate of change is negative when the function is decreasing. In the case of h(x) = x^2 - 1, which is a parabola opening upwards, the function decreases as x moves from the left to the right towards the vertex. Therefore, the interval in which the function has a negative average rate of change is from x = -∞ to x = 0, because this is where the function values are falling. To find the average rate of change between two points x1 and x2, we can use the formula: (h(x2) - h(x1)) / (x2 - x1). If x1 is to the left of the y-axis (x1 < 0) and x2 is the y-axis (x2 = 0), we will get a negative result since h(x2) < h(x1) in that interval, showing a negative average rate of change.

The function h(x) = x^2 - 1 has a negative average rate of change over the interval − 3 ≤ x ≤ 1. This interval includes the vertex of the parabola at x = 0, where the function is decreasing, resulting in a negative rate of change.

The function h(x) = x2 - 1 has different average rates of change depending on the interval we are considering. To find an interval where the average rate of change is negative, we need to look at intervals where the function is decreasing. The function h(x) will be decreasing on any interval that includes the value x = 0 since this is where the vertex of the parabola represented by h(x) is located, and it is a parabola opening upwards.

Analyze intervals around x = 0 to find where the function decreases. Looking at Choice C (−3 ≤ x ≤ 1), we can calculate the average rate of change as:

Since the average rate of change is negative (-2), Option C is the interval over which h(x) has a negative average rate of change.

the complete Question is given below:

h(x)=x 2 −1h, left parenthesis, x, right parenthesis, equals, x, squared, minus, 1 Over which interval does h hh have a negative average rate of change? Choose 1 answer: Choose 1 answer: (Choice A) A − 3 ≤ x ≤ 5 −3≤x≤5minus, 3, is less than or equal to, x, is less than or equal to, 5 (Choice B) B 1 ≤ x ≤ 4 1≤x≤41, is less than or equal to, x, is less than or equal to, 4 (Choice C) C − 3 ≤ x ≤ 1 −3≤x≤1minus, 3, is less than or equal to, x, is less than or equal to, 1 (Choice D) D − 1 ≤ x ≤ 5 −1≤x≤5minus, 1, is less than or equal to, x, is less than or equal to, 5 Show Calculator

Answer:

The solution for x is (-∞, 3).

Step-by-step explanation:

The provided inequality is: [tex]4x-2<10[/tex]

Solve for x a follows:

[tex]4x-2<10\\\\Add\ 2\ to\ both\ sides\\\\4x-2+2<10+2\\\\4x<12\\\\Divide\ both\ sides\ by\ 4\\\\\frac{4x}{4}<\frac{12}{4}\\\\x<3[/tex]

The range of the values of x is

[tex]x<3\\This\ implies\ that\ x\ belongs\ to\ the\ interval\ (-\infty, 3)[/tex]

Thus, the range of the values of x is (-∞, 3).

Answer:

x = m+-4

Step-by-step explanation:

We are trying to figure out the slope and the slope equals m, Then we have the y-intercept which that equals -4

Answer:

102

Step-by-step explanation:

Nat had a total of 102 stamps which he divided into 17 sets. Each set contained six stamps.

To find out how many stamps Nat had, we need to multiply the number of sets by the number of stamps per set. Nat divided his stamps into sets of six. He made 17 sets. To calculate the total number of stamps, we perform the multiplication:

Multiply the number of stamps in each set (6) by the number of sets (17).

6 stamps/set × 17 sets = 102 stamps
Hence, Nat had 102 stamps in total.

Answer:

45°

Step-by-step explanation:

90-45=45°

Answer:

Kwame's team will save = 7.8 [tex]\times[/tex] $0.24 = $1.87

Step-by-step explanation:

i.) Let the side of the equilateral triangle base be a

ii.) the area of the base = 3.9 square feet

iii.) the area of equilateral triangle is = [tex]\frac{\sqrt{3} }{4} a^{2}[/tex] = 3.9

iv.) Base area  = 3.9 square feet

v.) The area that is not covered is the base.

vi.) The total area that is not covered  = 3.9 [tex]\times[/tex] 2  since there are two pyramids

    therefore the total area not covered = 7.8 square feet

vii.) therefore Kwame's team will save = 7.8 [tex]\times[/tex] $0.24 = $1.87

Final answer:

To find the height of a cylinder with a known radius and surface area, subtract the area of the bases from the total surface area to get the lateral surface area, and then solve for the height. Using the surface area formula SA = 2πr² + 2πrh, the height is computed to be approximately 9.4 cm.

Explanation:

To calculate the height of a cylinder when you know its surface area and radius, you use the surface area formula for a cylinder, SA = 2πr² + 2πrh, where SA is the surface area, r is the radius, and h is the height of the cylinder. Given that the surface area (SA) is 1,220 cm² and the radius (r) is 10 cm, the formula can be rearranged to solve for h (height). The first step is to calculate the area of the circular bases, which is 2πr², then subtract this value from the total surface area to get the lateral surface area (2πrh), and finally divide by (2πr) to solve for h.

First, calculate the area of the circular bases:

Area of one base = πr² = 3.14159 × 10² cm² = 314.159 cm²

Total area of both bases = 2 × 314.159 cm² = 628.318 cm²

Subtract this from the total surface area to find the lateral surface area:

Lateral surface area = SA - area of bases = 1,220 cm² - 628.318 cm² = 591.682 cm²

Finally, solve for the height:

2πrh = 591.682 cm²

h = 591.682 cm² / (2 × 3.14159 × 10 cm)

h ≈ 9.4 cm

Thus, the height of the cylinder is approximately 9.4 cm.

The height is approximately 9.42 cm.

To find the height of a cylinder when given the radius and the surface area, use the formula for the surface area of a cylinder: [tex]SA = 2\pi r^2+2\pi rh[/tex]. Here, we know the surface area (SA) is 1220 [tex]cm^2[/tex], and the radius (r) is 10 cm.

First, let's write down the formula with the given values:

[tex]1220 = 2\pi (10)^2 + 2\pi (10)h[/tex]

We can simplify the equation step by step:

Therefore, the height of the cylinder is approximately 9.42 cm.

Answer:

13

Step-by-step explanation:

Circumference=2πr

2πr=26π

2r=26

r=13

Final answer:

The radius of a bicycle wheel that travels 26π inches per revolution is found using the circumference formula. By solving 26π = 2πr, the radius is determined to be 13 inches.

Explanation:

The question asks to determine the radius of a bicycle wheel that travels 26π inches per revolution. To find the radius, we can use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference and r is the radius. Since we know the wheel travels 26π inches for each revolution, this distance is the circumference of the wheel.

Setting up the equation 26π = 2πr, we can solve for the radius r by dividing both sides of the equation by 2π:

The radius of the bicycle wheel is 13 inches.

Answer:2

Step-by-step explanation:

a. Perimeter

b. Volume

c.Suface Area

Answer:

171

Step-by-step explanation:

(133+206+x)/3 = 170

133+206+x = 510

339 + x = 510

x = 171

(133+206+171)/3 =