7. (a) A homeowner wishes to replace the three identical steps leading to her front door with a ramp. Each step is 10 cm high and 35 cm long. Find the length of the ramp. Give your answer correct to one decimal place.​

Answer:

D. 20/29

Step-by-step explanation:

The sine of an angle in a right triangle is the ratio between the side opposite to the angle and the side adjacent to the angle, or [tex]sin(a) = \frac{opposite}{hypotenuse}[/tex]. The hypotenuse is the longest side of a right triangle.

In this case, the opposite side has length 20, and the hypotenuse has length 29. Therefore, the answer is

[tex]sin(a) = \frac{20}{29}[/tex].

To remember this (and the other trigonmetric ratios), you can use the acronym SOCAHTOA, where

SOH is sin(a) = opposite/hypotenuse

CAH is cos(a) = adjacent/hypotenuse

TOA is tan(a) = opposite/adjacent

Answer: 8

Step-by-step explanation:

Arrange the data in ascending order, and the median is the middle value. If the number of values is an even number, the median will be the average of the two middle numbers.

Rearrange 9, 9, 2, 8, 11, 6, 4 in ascending order:

2, 4, 6, 8, 9, 9, 11

The number eight appears to be in the very middle, therefore it is the median.

Answer:

6x/4×10x/3× x/6

5x^3/6

Therefore, Mr. Tompkins lives 240 miles from the airport.

Acceleration is the rate of change of velocity of an object. It is a vector quantity that has both magnitude and direction. Mathematically, it is the derivative of velocity with respect to time. In simpler terms, it is the change in speed or direction of an object over time.

Velocity is a vector quantity that describes the rate of change of an object's position. It has both magnitude and direction. The magnitude of velocity is the speed of an object, which is the distance covered per unit of time.

We can start solving the problem by using the formula: distance = speed x time.

Let x be the distance from Mr. Tompkins' home to the airport in miles.

Therefore, the distance from the airport to the other city is (670 - x) miles

we know that the total traveling time is 4 hours

so we can set up two equations:

x/30 + (670 - x)/250 = 4

x + (670 - x)/8 = 120

we can solve for x

x = 240 miles

Therefore, Mr. Tompkins lives 240 miles from the airport.

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Answer:

120

Step-by-step explanation:

6 x 20 = 120

Answer:

1. A simple cashier working at a supermarket

2. Doctors/medical professionals

Step-by-step explanation:

Although usually simple the cashiers must be able to do basic math to be able to give the correct amount of change to the customer

Medical professionals are constantly converting measurements in the workplace needing math to help with their cases

Answer:

1. Doctors regularly analyze numbers, make computations and employ statistics or to find the success rate of treatments. Math skills also are important when analyzing X-rays and CAT scans.

2. Electrical engineers use math in many ways in their career. They use math to help design and test electrical equipment. They use math to calculate amp and volt requirements for electrical projects. They use math in creating computer simulations and designs for new products.

Step-by-step explanation:

And math teaches other important practices, including how to approach tasks methodically, pay attention to detail, and think abstractly. Science, technology, and engineering disciplines, for example, rely heavily on mathematics.

Answer:

56

Step-by-step explanation:

180-124 ....................

Answer:

Step-by-step explanation:

So first you going to multiply the 1 by the 5 yd then divide that 3 by how many blocks there are and then add your answer of 40

Answer:

D. $69,160

Step-by-step explanation:

40,820(10) - 33,904(10) = 408,200 - 339,040 = 69,160

Answer:

1.Runner A is faster than Runner B.

2.Runner B has a head start.

Step-by-step explanation:

1. Runner A is at a further position (has a higher y), when both A and B have the same X(time)

2.At an X of 0(start) B has a further position (higher X)

I hope this helps you :)! Have a nice day.

Answer:

C. (0, 2)

Step-by-step explanation:

The solution to the systems of linear equations is the coordinates of the point (x, y) where both lines of the equations intercept each other on the graph given.

Thus, the lines intercept at the point where when x = 0, y = 2.

Therefore, the solution = (0, 2).

Yes. The flowerbed is √45 feet away from the sprinkler, which is less than the 7-foot radius.

Given that,

Based on the above information, the calculation is as follows:

[tex]= \sqrt(3^2 + 6^2) \\\\= \sqrt45[/tex]

= 6.7m

Therefore the above statement should be considered true.

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Answer:

It should be D

Step-by-step explanation:

Answer: -26

Step-by-step explanation:

edge 2021

21, 19, 25, 23

Step-by-step explanation:

I hope this helps!

Answer: it's the third answer

Step-by-step explanation:

yes, the two triangles are right angled triangles

The equivalent expression of log₁₂(x⁴√x³) - 2(x+1)⁵ is 11/2log₁₂(x) - 2(x+1)⁵

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

log 12 x^ 4 sqrt x^ 3 -2 (x+1)^ 5 ?

Express properly

So, we have the following representation

log₁₂(x⁴√x³) - 2(x+1)⁵

Evaluate the exponent

log₁₂(√x¹¹) - 2(x+1)⁵

Apply the power rule of logarithm

This gives

11/2log₁₂(x) - 2(x+1)⁵

Hence, the equivalent expression is 11/2log₁₂(x) - 2(x+1)⁵

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Answer:

The 90% confidence interval for the mean difference in pulse rates for the population of study participants is between -2.9 beats per minute and 0.5 beats per minute.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 10 - 1 = 9

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.8331

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 1.8331\frac{2.97}{\sqrt{10}} = 1.7[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is -1.2 - 1.7 = -2.9 beats per minute

The upper end of the interval is the sample mean added to M. So it is -1.2 + 1.7 = 0.5 beats per minute.

The 90% confidence interval for the mean difference in pulse rates for the population of study participants is between -2.9 beats per minute and 0.5 beats per minute.

On solving the provide question, we can say that - the quadratic equation [tex](6a^2 + 4b)(a^2 - b)[/tex] = -4

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

here, we have

[tex](6a^2 + 4b)(a^2 - b)[/tex]

a = 0 and b = 1

-4

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Answer:

x = 250°

Step-by-step explanation:

"Angle formed between a chord and tangent intersecting on a circle measure the half of the intercepted arc"

From the figure attached,

Angle between the chord and the tangent = 55°

Measure of intercepted arc (minor arc AB) = h°

Therefore, 55° = [tex]\frac{1}{2}(h)[/tex]

[tex]h=110^0[/tex]

And m(minor arc AB) + m(major arc AB) = 360°

h° + x° = 360°

110° + x° = 360°

x° = 360° - 110°°

x = 250°

Therefore, measure of the intercepted arc is 250°.

Answer:

B. 8 servings

Step-by-step explanation:

1 quart = 4 cups

3x4=12

3 quarts of clam chowder = 12 cups of chowder

1 1/2 cups each

12 divided by 1 1/2 = 12 divided by 3/2 = 12 divided by 2/3 = 8 servings

Answer:

10.8% increase

Step-by-step explanation:

($0.70/$6.50) x 100 = 10.769% = 10.8%

Answer:

420 m2

Step-by-step explanation:

Hope this helps

The surface area of the prism will be equal to 366 square meters.

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any object is called the surface area.

Given that:-

The surface area of the prism will be calculated as:-

Surface area = Sum of the area of all sides

There are three rectangle faces and two triangular faces in the triangular prism.

Surface area = 3 ( area of rectangle) + 2 (area of triangle)

Suraface area= 3 ( 10 x 9 ) + 2 [( 1/2)(16 x 6)]

Surface area = 270 + 96 = 366 square meter.

Therefore the surface area of the prism will be equal to 366 square meters.

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Answer: D. 12,330 phones

Step-by-step explanation:

First remove the fixed cost from the operating budget so that the variable cost that can be spent on each phone is known in total:

= 951,615 - 225,378

= $726,237

With each phone costing $58.90, the total number of phones that can be produced is therefore:

= Variable budget / Variable cost per phone

= 726,237 / 58.90

= 12,330 phones