i need help with this prblem

Answer:

The surface area of a rectangular prism is given by the formula:

SA = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the prism, respectively. We are given that the surface area of the prism is 1,060 cm², and that the base has measurements 8 cm and 10 cm.

Substituting these values into the formula, we get:

1060 = 2(8)(10) + 2(8)h + 2(10)h

Simplifying and solving for h, we get:

1060 = 160 + 16h + 20h

1060 = 160 + 36h

900 = 36h

h = 25

Therefore, the height of the prism is 25 cm.

Step-by-step explanation:

Differentiating y = x^3 ln 2x/e^x Sin x is: y' = x^2 [(3 ln 2x/e^x Sin x + 3/x) - 2 ln 2x/e^x Sin x cos x + cos x].

Differentiate y can be find using the product and chain rule.

Using the chain rule

v'(x) = [1/(2x/e^x)] * (2e^x - e^x*2x) / (2x/e^x)^2

v'(x) = [e^x(2-e^x)] / (2x)^2

Using the product rule

y' = 3x^2 ln(2x/e^x) sin(x) + x^3 [e^x(2-e^x)] / (2x)^2 sin(x) + x^3 ln(2x/e^x) cos(x)

Simplifying

y' = 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x)

So,

derivative of y is:

y' = 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x)

Therefore the differentiate of y is 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x).

Learn more about differentiation here:https://brainly.com/question/25081524

#SPJ1

Answer:

92.

Step-by-step explanation:

To find the range of the set of numbers 20, 3, 95, 54, 71, 66, we first need to find the difference between the largest and smallest numbers in the set.

Largest number = 95

Smallest number = 3

Range = Largest number - Smallest number

Range = 95 - 3

Range = 92

Therefore, the range of the set of numbers 20, 3, 95, 54, 71, 66 is 92.

Answer:92

Step-by-step explanation: highest-lowest

it helps to put the terms in order first

95-3=92

Answer: 7

Step-by-step explanation: he spends 7 hours a day take 3 away from 10.

The radius of the circle is approximately 7.9 feet.

The arc length formula (if θ is in degrees) is expressed as:

s = 2πr × (θ/360°)

Where r is radius and θ is the central angle subtended by the arc.

Given that:

Arc length s = 9ft

Central angle subtended by the arc = 65°

Radius r = ?

Plug the given values into the above formula.

s = 2πr × (θ/360°)

9ft = 2 × 3.14 × r × (65/360°)

r = 9ft / 1.133888

r = 7.9 ft

Therefore, the radius is 7.9 ft.

Learn more about arc of length here: https://brainly.com/question/16403495

#SPJ1

There are 27.558 meters of wire does she have remaining after the first day.

We have to given that;

An electrician has 42.3 meters of wire to use on a job.

And, On the first day, she uses 14.742 meters of the wire.

Hence, We get;

The remaining wire does she have remaining after the first day is,

⇒ 42.3 - 14.742

⇒ 27.558 meters

Thus, There are 27.558 meters of wire does she have remaining after the first day.

Learn more about the subtraction visit:

https://brainly.com/question/17301989

#SPJ1

The lengths arranged from shortest to longest is [tex]2\frac{7}{8}[/tex],  [tex]3\frac{1}{4}[/tex], [tex]3\frac{1}{2}[/tex] , [tex]3\frac{5}{6}[/tex], [tex]4\frac{2}{3}[/tex] (option H).

The lengths of the woods are expressed as mixed numbers. Mixed numbers are non-integers that consists of a whole number and a proper fraction. For example, [tex]3\frac{1}{4}[/tex] is a mixed number. 3 is the whole number and [tex]\frac{1}{4}[/tex] is the proper fraction.

In order to arrange the lengths of the woods from shortest to the longest, convert the mixed numbers to decimals for easy comparison.

[tex]3\frac{1}{4}[/tex] becomes 3.25

[tex]2\frac{7}{8}[/tex] becomes 2.875

[tex]3\frac{5}{6}[/tex] becomes 3.833

[tex]4\frac{2}{3}[/tex] becomes 4.667

[tex]3\frac{1}{2}[/tex] becomes 3.5

The lengths arranged from shortest to longest is [tex]2\frac{7}{8}[/tex],  [tex]3\frac{1}{4}[/tex], [tex]3\frac{1}{2}[/tex] , [tex]3\frac{5}{6}[/tex], [tex]4\frac{2}{3}[/tex]

To learn more about fractions, please check: https://brainly.com/question/25779356

#SPJ1

Answer: 76 cubic feet

Step-by-step explanation:

Think about breaking it into two rectangular prisms:

Total volume = Volume of longer prism + volume of shorter prism

Total volume = 8x4x2 + 2x2x3

Total volume = 76 cubic feet

The measure of the central angle is 0.75 radians

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

The length of an arc with an angle of Ф is given by:

Length of arc = (Ф/360) * (π * diameter)

The diameter is 16 cm and intercepted arc length is 6 cm, hence:

Length of arc = (Ф/360) * (π * diameter)

6 = (Ф/360) * (π * 16)

Ф = 42.97°

Ф = 42.97° * π/180 = 0.75 radian

The measure of the central angle is 0.75 radians

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

[tex]\cfrac{10}{x}=\cfrac{x}{7}\implies 70=x^2\implies \sqrt{70}=x[/tex]

32 is the number of teams took less than 20minutes to complete the game

Given that Isaac measured the time it took for some teams to complete an escape room game.

The times were recorded in the table

We have to find the number of teams which are  less than 20minutes to complete the game

Number of teams took less than 20 minutes

=8+24

=32

Hence, 32 is the number of teams took less than 20minutes to complete the game.

To learn more on Statistics click:

https://brainly.com/question/30218856

#SPJ1

Answer:

To find the mean of the data, we add up all the heights and then divide by the number of players:

Mean = (58 + 60 + 61 + 59 + 63) / 5

Mean = 301 / 5

Mean = 60.2 inches

Therefore, the mean height of the players on the Tracy basketball team is 60.2 inches.

The answer is 60.2in.

Step-by-step explanation:

Option C is the true statement from the data that has been gathered and shown in the image

The interquartile range exemplifies the "dispersion" or width of a set [1] by determining the difference between the top quartile (the 25% highest) and lower quartile (the 25% lowest). In reference to the provided picture:

- The bus drivers' interquartile range is 10, represented by subtracting their distance's lowest point (10) from the highest (20).

20 - 10 = 20

- Similarly, the teachers' interquartile range is 15, which stems from finding the difference between their lowest distance (15) and highest distance (30).

30 - 15 = 15

Therefore, comparing both ranges reflects that the bus drivers have an interquartile range of distances that is 5 miles smaller than the one for the teachers. Consequently, we opt for option C.

Read more on interquartile range here: https://brainly.com/question/4102829

#SPJ1

Answer:

85.84

Step-by-step explanation:

6x4 is the area of 1 rectangle

There r 3 rectangles

6x4 =24

24x3 =72

That’s the area if all the rectangles

There r 2 triangles

(4x3.46)/2 is the area of 1 triangle

=6.92

6.92x2 =13.84

total surface area is all the areas added up

72+13.84

=85.84

Answer:

The value of x is 10√2, so A is correct.

Step-by-step explanation:

In an isosceles right triangle, the length of the hypotenuse is √2 times the length of a leg. Since each leg has length 10, the hypotenuse has length 10√2. A is correct.

The amount of money that Nora would need to invest is $25913.

In Mathematics and Financial accounting, compound interest can be calculated by using the following mathematical equation (formula):

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where:

By substituting the given parameters into the formula for compound interest, we have the following;

[tex]72,000 = P(1 + \frac{0.064}{365})^{365 \times 16}\\\\72,000 = P(1 + 1.75 \times 10^{-4})^{5,840}\\\\72,000 = P(1.000175)^{5,840}[/tex]

P = 72,000/2.77849825425152

Principal, P = $25913.28 ≈ $25913

Read more on compound interest here: brainly.com/question/16608367

#SPJ1

The requried lottery commission should make a single deposit of Kenya Shillings 8.7475 million (rounded to 4 decimal places) to fund Peter's annuity.

To calculate the present value of Peter's annuity,

[tex]PV = PMT * (1 - (1 + r)^{-n}) / r[/tex]

where PV is the present value, PMT is the monthly payment, r is the monthly interest rate, and n is the number of months.

In this case, PMT = 87325, r = 0.107/12 = 0.008917, and n = 21*12 = 252.

Substitute the value in the formula given above:

[tex]PV = 87325 * (1 - (1 + 0.008917)^{-252} / 0.008917[/tex]

PV = 8747531.78

Thus, the lottery commission should make a single deposit of Kenya Shillings 8.7475 million (rounded to 4 decimal places) to fund Peter's annuity.

Learn more about PMT here:

https://brainly.com/question/31325062

#SPJ1

Answer:

mean=5

Step-by-step explanation:

To find the mean of a set of data, we add up all the values in the set and then divide by the number of values.

Adding up the values in the set, we get:

3 + 5 + 4 + 4 + 5 + 7 + 7 = 35

There are 7 values in the set, so we divide the sum by 7 to get the mean:

mean = sum of values / number of values

mean = 35 / 7

mean = 5

Answer:16x-4-2x+8=14x+4

Step-by-step explanation:

In order to solve this question you first want to multiply everything inside the bracket by the number outside.

4(4x-1)

so 4 times 4x which is 16x and 4 times -1 which is -4 so the first bracket is

(16x-4)

then do the same for the second bracket

-2(x-4)

so -2 times x would be -2x and -2 times -4 would be 8

for the final step collect the like terms and solve

so your answer would be

16x-2x which would be 14x and -4+8 which would be 4

so in conclusion the answer is

14x+4

If the "angle M" measures 98° and "angle N" measures (6x + 2)°, then value of "x" must be 16.

When the "two lines" intersect, the opposite angles formed are equal in measure, which means that vertical angles are congruent. So, we have:

⇒ Angle M = Angle N

Using the given values, we can write an equation:

⇒ Angle M = 98°  and Angle N = (6x + 2)°,

Setting them equal,

We get,

⇒ 98 = 6x + 2,

Solving for x, we subtract 2 from both sides and then divide by 6:

⇒ 96 = 6x,

⇒ x = 16,

Therefore, the variable "x" must be 16 for "angle N" to be vertical to "angle M".

Learn more about Angle here

https://brainly.com/question/20334114

#SPJ1

The given question is incomplete, the complete question is

If an "angle N" is vertical to "angle M", and measure of "angle M" is 98° and the measure of angle N is (6x + 2)°, the x must be.

The polar coordinate (3, 45°) lies in the same location on the polar plane as (-3, Ø), where -360° < Ø < 0. Then, the value of Ø is 45°.

The polar coordinates (r, θ) represent a point on the polar plane, where r is the radial distance from the origin (in this case, 3 units) and θ is the angle measured counterclockwise from the positive x-axis (in this case, 45°).

According to the given statement, the polar coordinate (-3, Ø) lies in the same location on the polar plane as (3, 45°). This means that these two points represent the same location, and their radial distances and angles must be equivalent.

Comparing the radial distances;

|r| = 3 (for (3, 45°))

|-r| = 3 (for (-3, Ø))

Since |-r| = |r|, we can conclude that r = -r, which implies r = 0, as r cannot be negative in polar coordinates.

Comparing the angles;

θ = 45° (for (3, 45°))

θ = Ø (for (-3, Ø))

Since the angles are equivalent, we can equate them:

45° = Ø

To know more about polar coordinate here

https://brainly.com/question/25360680

#SPJ1

Answer:

To go from ABC to DEF, you have to multiply by 8/9

Step-by-step explanation:

40/45 = 8/9

88/99 = 8/9

80/90 = 8/9

Answer:

Let's set up a system of equations to solve for S and L:

S + L = 24 (they sold a total of 24 shirts)

14S + 17L = 378 (the total amount made from selling the shirts was $378)

We can solve for one variable in the first equation and substitute it into the second equation:

S = 24 - L

14(24 - L) + 17L = 378

336 - 14L + 17L = 378

3L = 42

L = 14

So they sold 14 long sleeve shirts. We can substitute this value back into the first equation to solve for S:

S + 14 = 24

S = 10

Therefore, they sold 10 short sleeve shirts and 14 long sleeve shirts.

The possible combinations of hand pies and gourmet cupcakes that the baker could sell for exactly $45.00 are:

The possible combinations of hand pies and gourmet cupcakes can be determined by finding the results of each combination using multiplication and addition.

Multiplication and addition are two of the four basic mathematical operations, including division and subtraction.

The unit cost of hand pies = $5

The unit cost of cupcakes = $3

The total sales revenue = $45

a. No hand pies and 15 gourmet cupcakes = $45 ($5 X 0 + $3 x 15)

b. 2 hand pies and 11 gourmet cupcakes = $43 ($5 X 2 + $3 x 11)

c. 3 hand pies and 10 gourmet cupcakes = $45 ($5 X 3 + $3 x 10)

d. 5 hand pies and 6 gourmet cupcakes = $43 ($5 X 5 + $3 x 6)

e. 6 hand pies and 5 gourmet cupcakes = $45 ($5 X 6 + $3 x 5)

f. 8 hand pies and 2 gourmet cupcakes = $46 ($5 X 8 + $3 x 2)

g. 9 hand pies and no gourmet cupcakes = $45 ($5 X 9 + $3 x 0)

Learn more about mathematical operations at https://brainly.com/question/4721701.

#SPJ1

Answer:

Kenyon could make a total of 7 bouquets.

Step-by-step explanation:

To find the greatest number of bouquets we need to find GCF.

We need to find GCF for 21 and 28.

The factors of 21 are: 1,3,7, and 21.

The factors of 28 are: 1,2,4,7,14, and 28

1 and 7 are the common factors between 21 and 28.

From the factors, the greatest common factor is 7.

Answer:

28 hours

Step-by-step explanation:

Let's use "B" to represent the number of hours Bianca practiced.

From the problem, we know that Filipe practiced 12 fewer hours than Bianca, which means:

Filipe's practice time = Bianca's practice time - 12

We are also told that Filipe practiced for 16 hours, so we can substitute that into the equation:

16 = B - 12

To solve for B, we can add 12 to both sides:

16 + 12 = B

So, Bianca practiced for a total of 28 hours.

The function f(x) = 3x/(x-9) has a vertical asymptote at x=9, a horizontal asymptote at y=3 as x->±∞, and a horizontal asymptote at y=-3 as x->±∞.

To identify the asymptotes and state the end behavior of the function f(x) = 3x/(x-9), we need to analyze the behavior of the function as x approaches positive and negative infinity.

First, let's look at the denominator of the fraction, which is x-9. This means that the function has a vertical asymptote at x=9, as the denominator approaches zero at that point. This vertical asymptote divides the x-axis into two regions, x<9 and x>9.

Now let's consider the behavior of the function as x approaches positive infinity. In this case, the numerator grows faster than the denominator, and the function approaches a horizontal asymptote at y=3. To see this, we can use the limit definition:

lim (x->∞) f(x) = lim (x->∞) 3x/(x-9) = lim (x->∞) 3(1/(1-9/x)) = 3

Similarly, as x approaches negative infinity, the function also approaches a horizontal asymptote at y=-3. Again, we can use the limit definition to confirm this:

lim (x->-∞) f(x) = lim (x->-∞) 3x/(x-9) = lim (x->-∞) 3(1/(1-9/x)) = -3

Therefore, the function f(x) = 3x/(x-9) has a vertical asymptote at x=9, a horizontal asymptote at y=3 as x->±∞, and a horizontal asymptote at y=-3 as x->±∞.

To learn more about asymptote click on,

https://brainly.com/question/28829971

#SPJ1

An equation for the height of the rocket after t seconds is h(t) = -16t² + 352t.

The time it takes for the rocket to reach a height of 0 is 22 seconds.

The time it takes to reach the top of its trajectory is 11 seconds.

The maximum height is 1,936 feet.

The time it takes to reach a height of 968 feet is 18.8 or 3.2 seconds.

Based on the information provided, we can logically deduce that the height (h) in feet, of this rocket above the​ ground is related to time by the following quadratic function:

h(t) = -16t² + Vit

When the initial velocity is 352 feet per seconds, the height function becomes;

h(t) = -16t² + 352t

Generally speaking, the height of this rocket would be equal to zero (0) when it hits the ground. Therefore, we would equate the height function to zero (0) as follows:

0 = -16t² + 352t

352t = 16t²

Time, t = 352/16

Time, t = 22 seconds.

Next, we would determine the maximum height of this rocket by taking the first derivate in order to determine the time (t) it takes;

h(t) = -16t² + 352t

h'(t) = -32t + 352

352 = 32t

t = 352/32 = 11 seconds.

h(11) = -16(11)² + 352(11)

h(11) = 1,936 feet.

At a height of 968 feet, the time is given by;

968 = -16t² + 352t

16t² - 352t + 968 = 0

t² - 22t + 60.5 = 0

Time, t = 18.8 or 3.2 seconds.

Read more on time here: brainly.com/question/26746473

#SPJ1