The base of 12-foot ladder is 6 feet from a building. If the ladder reaches the flat​ roof, how tall is the​ building?

Answer:

Step-by-step explanation:

5+3x/4 = 7/12

[(5*4)+3x]/4 = 7/12

(20+3x)/4 = 7/12

20+3x = 7/12*4

20+3x = 7/3

3x = 7/3 - 20

3x = [7-(20*3)]/3

3x = (7-60)/3

3x = -53/3

x = -53/3/3/1 ( reciprocal )

x = -53/3*1/3

x= -53/9

The length of the side on the prism is 5cm. The area of the shaded region is 72 cm².

Area is the total amount of area occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the region that its boundary encloses. The quantity of unit squares that span a closed figure's surface is its area. Square units like cm² and m² are used to quantify area. A shape's area is a two-dimensional measurement.

The region inside the perimeter or boundary of a closed shape is referred to as the "area". Such a shape has at least three sides that can be joined together to create a boundary. The "area" formula is used in mathematics to describe this type of space symbolically.

In this figure,

The 5cm flap will be adjacent to the side x. Therefore,

Length of the side x= 5cm

Area of the shaded region= l×b

because the shaded region is a rectangle.

area= 9*x

       =9*5= 45 cm²

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a. Two levels of factor B were used in the experiment.

b. The degrees of freedom associated with interaction are 50.

c. The error mean square is 6.00. d. The mean square for factor A is 175.00.e. The experiment was conducted with three replicates.f. The interaction is significant. Factor A is significant. Factor B is not significant.g. An estimate of the standard deviation of the response variable is 2.449. h. If the experiment had been run in blocks (CRBD) there would have been 12 degrees of freedom for blocks.Solution:Factorial design: A factorial design is an experimental design that consists of two or more factors, each with two or more levels, and each subject is assigned to one and only one level of each factor. The objective of a factorial experiment is to analyze the effect of each factor on the response variable and to examine if there is any interaction between factors.a. Two levels of factor B were used in the experiment.b. Interaction degrees of freedom = AB = 50.c.

Mean square for error: MSE = 150/10 = 15.d. Mean square for factor A: MS(A) =[tex]SSA/dfA = 350/2 = 175.e.\\[/tex] Three replicates were conducted (from the error df = 10).f. Interaction is significant. Factor A is significant. Factor B is not significant.g. Estimate of the standard deviation of the response variable: sqrt(15/2) = 2.449.h. If the experiment had been conducted in a CRBD, there would have been 12 degrees of freedom for the block.

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Answer:

The other leg is 5.4 cm

Step-by-step explanation:

We are given that in a triangle, the hypotenuse is 15cm, and one of the legs is 14cm.

We want to find the length of the other leg.

The Pythagorean Theorem states that a² + b² = c², where a and b are the legs and c is the hypotenuse.

We can substitute what we know into the theorem.

14² + b² = 15²

196 + b² = 225

Subtract.

b² = 29

Take the square root of b to get:

b = √29 cm

√29 ≈ 5.4 cm

The probability that it the marble taken out of the box is not blue is [tex]\frac{112}{131}[/tex].

Probability is a branch of math that studies the chance or likelihood of an event occurring.
There are [tex]75[/tex] red marbles, [tx]37[/tex] white marbles, and [tex]19[/tex] blue marbles.

If a marble is randomly selected from the box, we have to find the probability that it is not blue.

Then the total number of marbles = [tex]75 + 37 + 19 = 131.[/tex]

The probability that a marble is not blue:-

[tex]P[/tex](Not blue) = [tex]P[/tex](Red or White)

[tex]P[/tex](Red or White) = [tex]\frac{(75 + 37)}{131}[/tex]

[tex]P[/tex](Red or White) = [tex]\frac{112}{ 131}[/tex]

[tex]P[/tex](Not blue) = [tex]1 - P[/tex](Blue)

[tex]P[/tex](Not blue) = [tex]1 - \frac{19}{131}[/tex]

[tex]P[/tex](Not blue) = [tex]\frac{112}{ 131}[/tex]

Therefore, the probability that a marble selected from the box is not blue is [tex]\frac{112}{131}[/tex].

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2/7 + 1/4 = 15/28 ≅ 0.5357143

Add: 2/7 + 1/4 = 2 · 4/7 · 4 + 1 · 7/4 · 7 = 8/28 + 7/28 = 8 + 7/28 = 15/28 

It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(7, 4) = 28. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 4 = 28. In the following intermediate step, it cannot further simplify the fraction result by canceling.In other words - two sevenths plus one quarter is fifteen twenty-eighths.

Answer:

3 pounds of coffee.

Step-by-step explanation:

Equation

y = -7.37x + 80  

substitute 57.89 for y

57.89 = -7.37 + 80   Subtract 80 from both sides

57.89 - 80 = -7.37 + 80 - 80

-22.11 = -7.37x  Divide both sides by -7.37

3 = x

3 pound of coffee

Helping in the name of Jesus.

Answer:

rita received a $80 gift card for a coffee store. she used it in buying some coffee that cost $7.37 per pound. after buying the coffee, she had $57.89 left on her card. How many pounds of coffee did she buy?​

Step-by-step explanation:

Let's first find out how much money Rita spent on coffee:

$80 (initial balance) - $57.89 (remaining balance) = $22.11 spent on coffee

Now, let x be the number of pounds of coffee that Rita bought. Since the coffee costs $7.37 per pound, we can set up the equation:

$7.37x = $22.11

Solving for x, we can divide both sides by $7.37:

x = 3

Therefore, Rita bought 3 pounds of coffee.

The scale factor is 2 and center dilation is reduced.

The scale factor is a ratio that describes how much a figure has been enlarged or reduced. It is calculated by dividing the length of the corresponding sides of the original and dilated figures. If the scale factor is greater than 1, then the figure is enlarged, and if it is less than 1, then the figure is reduced.

To find the scale factor in an IXL dilations problem, you need to compare the corresponding sides of the original and dilated figures.

If the original figure has a side length of 4 units, and the dilated figure has a corresponding side length of 8 units, then the scale factor is 8/4=2. This means that the dilated figure is twice as large as the original figure.

The center of dilation is the point about which the figure is enlarged or reduced. It is the fixed point that remains unchanged during the dilation process.

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Answer: Associative property

Step-by-step explanation:

The definition of the associative property is the answer is the same no matter how the terms are grouped. Hope this helped!

To determine the probability of a continuous distribution we use the integral to determine it and for the normal distribution the integral is not so simple, for that reason it is simpler to use range values from tables.

Probability can be determined from a continuous distribution in the following way:To compute the probability of a given interval for a continuous random variable, the area under the curve over the interval is determined. Integrals are used to calculate this area under the curve, which can be done either numerically or analytically using probability density functions.

For some distributions, such as the uniform distribution, calculating the area under the curve is straightforward. However, for other distributions, such as the normal distribution, it can be more difficult to calculate the integral analytically.

The normal distribution is a continuous probability distribution that is frequently used in statistics. It is defined by its probability density function, which is a bell-shaped curve with a mean and a standard deviation.

Calculating the area under the curve for the normal distribution requires the use of integrals. Integrals are difficult to solve analytically for the normal distribution because the probability density function is not simple. However, it is relatively simple to calculate the probability for a given range of values using standard statistical tables or computer software.

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As per the given distance, the bus and the motorcycle will pass each other at 4:50 pm.

Now, let's find the distance the bus travels during that time. We know the speed of the bus is 60 mph, so we can use the formula distance = speed x time. Thus, the distance the bus travels is:

distance = speed x time

distance = 60 x t

Next, let's find the distance the motorcycle travels during the same time. The speed of the motorcycle is 72 mph, so we can use the same formula to find the distance the motorcycle travels:

distance = speed x time

distance = 72 x (t - 3/4)

Here, we subtract 3/4 from the time because the motorcycle leaves 45 minutes later than the bus. Remember, we need to convert 45 minutes to hours by dividing it by 60. Therefore, 45 minutes is equal to 3/4 of an hour.

Now that we have both distances, we can set them equal to each other since the bus and the motorcycle will meet at the same point in time:

60t = 72(t - 3/4)

Let's simplify and solve for "t":

60t = 72t - 54

12t = 54

t = 4.5

Therefore, it will take 4.5 hours for the bus and the motorcycle to meet each other. But, we need to find out what time that will be. We know the bus left at 12:20 pm, so we add 4.5 hours to that time:

12:20 pm + 4.5 hours = 4:50 pm

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The value of' b' is 27 when' a' is three.

The presented equation is a x 9 = b, wherein' a' is a variable and' b' is the product of' a' and nine. we are asked to find the value of' b' when' a' is 3.

Substituting the value of' a' into the equation, we get

3 x 9 = b

27 = b

Thus, the value of' b' is 27 when' a' is three.

On this equation,' a' is a variable, this means that that its cost can trade. still, the value of' b' is dependent on the price of' a'. whilst' a' is 3, the price of' b' is 27. this is an illustration of a easy linear equation, in which the value of one variable is dependent on the figure of any other variable, and can be used to model real-global situations.

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Answer:

None of the given options matches the value we got for x, but the closest option is A. 2 over 3. However, we need to note that x is not a whole number, it's a decimal.

Step-by-step explanation:

Let's solve the given equation

14x+312=2(12x+34)

Distribute the 2 on the right-hand side

14x+312=24x+68

Subtract 14x from both sides

312=10x+68

Subtract 68 from both sides

244=10x

Divide both sides by 10

x=24.4

Answer:

2 over 3

Step-by-step explanation:

none of the options match the value of x

Answer:

£11

Step-by-step explanation:

Let cost of jackets : x, DRESSES: y.

ATP,

2x+3y = 46 ...(1)

2x + 4y = 54 ...(2)

From 1, we get x = (46-3y)/2

By Substitution in (2), we get:

2(46-3y)/2 +4y = 54

=> 46-3y+4y= 54

=> x = 8

Thus, 1 dress cost: 46-3*8/2 = 46-24/2 =22/2 = £11

The probability that at most of the parts are defective is 0.96.

A machine that manufactures automobile parts produces defective parts of the time. If parts produced by this machine are randomly selected, what is the probability that at most of the parts are defective?

The given probability of producing defective parts is P(defective) = 0.15. Now, we need to find the probability that at most of the parts are defective. This can be done by finding the probability of producing 0, 1, or 2 defective parts.

Let X denotes the number of defective parts. So, we have to calculate the probabilities for P(X = 0), P(X = 1), and P(X = 2). To calculate these probabilities, we will use the binomial probability formula:

P(X = x) ={n}C{x} p^x (1 - p)^{n - x}, Here, n = number of parts produced, p = probability of producing defective parts

x = number of defective parts

First, we need to find P(X = 0),

P(X = 0) = (0.85)^5 = 0.4437

P(X = 1) = {5}C{1} (0.15)^1 (0.85)^4 = 0.3672

P(X = 2) = {5}C{2} (0.15)^2 (0.85)^3 = 0.1459

Now, we can find the probability that at most of the parts are defective as follows:

P{at most 2 defective parts}) = P(X = 0) + P(X = 1) + P(X = 2) = 0.957

Therefore, the probability that at most of the parts are defective is 0.96.

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First of all, perfect squares do not end in 2.

The exponent has to be an even number when 2 is the base. For example 2^8 = 64. 8 is an even number. So 64 is a square number.

13/12 will be long the next airplane model. This will be because her next model is to be 1/4 as long as the first.

Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be entire. When we cut a piece of cake in real life from the entire cake, the part represents the per cent of the cake. The word "fraction" is derived from Roman. "Fractus" means "broken" in Latin. The fraction was expressed verbally in earlier times. It was afterwards presented in numerical form.

Given,

The length of her first model is in the fraction [tex]4\frac{1}{3}[/tex]

As her next model has to be 1/4 as long as the first model

Therefore,

Length of her new or next model

1/4 of [tex]4\frac{1}{3}[/tex]

so, 1/4 * 13 / 3

13/12

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The surface area of the rectangular prism is 170 square yards.

Surface area is the total area of a three-dimensional shape's surface. Add the areas of all six faces to find the surface area of a cuboid with six rectangular faces. Alternatively, label the cuboid's length (l), width (w), and height (h) and use the formula: surface area (SA)=2lw+2lh+2hw.

To calculate the surface area of the rectangular prism, add the areas of each of its faces.

The front and back faces are 5 yards by 6 yards in size, so each has an area of:

5 yards x 6 yards equals 30 square yards

The top and bottom faces are 5 yards by 5 yards, so each has an area of:

5 yards x 5 yards equals 25 square yards

The two side faces have dimensions of 6 yards by 5 yards, for a total area of:

30 square yards = 6 yards x 5 yards

As a result, the surface area of the rectangular prism is as follows:

Front face area plus back face area plus top face area plus bottom face area plus left side face area plus right side face area

= 30+30+25+25+30+30

= 170 square yards

As a result, the rectangular prism has a surface area of 170 square yards.

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Step-by-step explanation:

9 b^2 c  = a     divide both sides of the equation by 9c

b^2 = a / (9c)    now take the sqrt of both sides

b = ± sqrt ( a/(9c) ) =   ± 1/3 sqrt ( a/c)  <====I do not see the correct answer posted....    perhaps one of the choices was transcribed incorrectly....

The following table shows how many hot cocoas Mei Mei would likely sell if the day's high temperature was 42 oF:

58.

How is a linear function defined?

The following is the definition of a linear function's slope and intercept:

y = mx + b.

The slope, or m, indicates the rate of change.

The value of y at x=0 is represented by the intercept, b.

At y = 100, where the function meets the y-axis, the intercept b is defined as follows:

b = 100.

As y decays to 94 when x rises to six, the slope m is calculated as follows:

m = (94 - 100)/(6 - 0) (6 - 0)

m = -1.

As a result, the function that forecasts how much hot chocolate will be sold at a high temperature.

Lack of Information

The graphic provided at the end of the response provides the linear function's graph.

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The triangle DEF is twice the size of the triangle ABC and the triangles are similar triangles

Given the triangles ABC and DEF

From the figure, we have

AB = 1

DE = 2

This means that the triangle DEF is twice the size of the triangle ABC

Yes, the triangles ABC and DEF are similar triangles

This is because the corresponding sides of  DEF is twice the corresponding sides of triangle ABC

Multipliying the coordinates of A by 2 gives coordinates of D

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Answer:

2x=5 > -14

Step-by-step explanation:

6(x - 2) -3 ≥ -4 ( -3 + 9) +10​
6x-12-3 > 12-36+10
6x-15 > -36+22
6x-15 > -14
6x=15 > -14
3    3        
2x=5 > -14

Answer:

[tex]{ \sf{ = 41 \times 100 + 41 \times { \boxed{2}}}} \\ \\ = { \sf{ \boxed{4100} + { \boxed{82}}}} \\ \\ = { \sf{ \boxed{4182}}}[/tex]

Answer:

A- 2

B- 4,100

C- 82

D- 4,182

The slope in the equation b = 0.29h + 1.35 is the measure of the rate at which the bike frame size changes with the height of the rider.

The slope in the equation b = 0.29h + 1.35 refers to the coefficient of the variable h, which represents the height of the rider. The slope is the measure of the rate at which the bike frame size changes with the height of the rider.

In this equation, the slope is 0.29, which means that for every inch increase in the rider's height, the bike frame size increases by 0.29 inches. The slope is a crucial component of the equation as it determines the proportionality of the two variables.

Moreover, the slope is essential in analyzing the relationship between the rider's height and the bike frame size.

It plays a vital role in determining the appropriate size of the BMX bike frame and analyzing the relationship between the two variables.

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Complete Question:

Purchasing the correctly sized BMX bike is based on the height of the rider. In order to fit a customer, the salesman can use the equation b 0.29h +1.35 where b is the size of the BMX bike frame in inches and h is the height of the rider in inches.

Which sentence explains the slope in the equation?

The probability that the sample proportion will be at least k is 0.7580.

Let P be the probability that any one person in the population will cooperate and respond to the questions. We are looking for the probability that at least k people out of n in the sample will cooperate and respond to the questions. Let X be the number of people who cooperate and respond to the questions in the sample. X follows the binomial distribution with parameters n and P.To calculate this, use the following formula:

Z = (X - μ) / σ

Here, X = number of people who cooperate and respond to the questions in the sample

μ = E(X) = np,  σ = sqrt(npq)

q = 1 - P

Now, to calculate the probability, first calculate μ = np =

σ = sqrt(npq)

Then, find the z-score using z = (k - μ) / σ.

Now, use the z-table to find the probability corresponding to the z-score obtained in the previous step. The probability obtained from the z-table is the probability that the sample proportion will be at least k.

The probability that the sample proportion will be at least k is 0.7580.

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The following points are matched:

Thus, the definitions are matched to their respective terms.

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Answer:

k

Step-by-step explanation:

2x+13<5x−20

Subtract 5x from both sides.

Combine 2x and −5x to get −3x.

Subtract 13 from both sides.

Subtract 13 from −20 to get −33.

Divide both sides by −3. Since −3 is negative, the inequality direction is changed.

​

x>11

The shape that results from connecting the points (-4, 1), (-4, -4), (0, 3), and (0, 6) is a trapezoid.

A trapezoid is a geometric form that has four sides, two of which are parallel and two of which are nonparallel (or skew lines). A trapezoid is also known as a trapezium (UK) or a trapeze (US).

The trapezoid's parallel sides are known as the bases, and the two nonparallel sides are known as the legs or lateral sides. The trapezoid is also sometimes referred to as the irregular quadrilateral.

A quadrilateral is a shape that has four sides, four vertices, and four angles. The following are the characteristics of a trapezoid:

The formula for the area of a trapezoid is as follows:

Area of a trapezoid = [ (base 1 + base 2) / 2 ] x height

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The new coordinates of the two points after rotating the parallel lines 180 degrees clockwise are (2, -7) and (-8, 5).

What are parallel lines?

In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet.

If the set of parallel lines contains the points (-2, 7) and (8, -5), then the two lines are parallel to each other and have the same slope. We can find the slope of the line that passes through these two points using the slope formula:

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

slope = (-5 - 7) / (8 - (-2))

slope = -12 / 10

slope = -6 / 5

So, the equations of the two parallel lines are:

y - 7 = (-6 / 5)(x + 2) --- equation 1

y + 5 = (-6 / 5)(x - 8) --- equation 2

To rotate the lines 180 degrees clockwise, we need to negate both the x and y coordinates of the points on the lines. That is, we need to replace each point (x, y) with the point (-x, -y).

So, after the rotation, the new coordinates of the two points will be:

(-(-2), -7) = (2, -7) --- for point (-2, 7)

(-(8), -(-5)) = (-8, 5) --- for point (8, -5)

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