An athlete has decided to track how many minutes they exercise each day. During the first day, the athlete exercised for 30 minutes. For each day after that, the athlete increased their exercise time by 3 minutes. Which equation in point-slope form models the number of minutes the athlete exercises, y, based on the day, x?

A: y-30=3(x-1)

B: y+30=3(x+1)

C: y-1=3(x-30)

E: y+1=3(x+30

Answer:

20 3/5

Step-by-step explanation:

this is the correct result when 30 9/10 is multipled by 2/3

Answer:

12 m

Step-by-step explanation:

Since this is a right triangle, let's use the Pythagorean Theorem.

Recall that the Pythagorean Theorem is:

[tex]a^2+b^2=c^2[/tex]

Where a is the length of one of the legs, b is the length of the other leg, and c is the length of the hypotenuse.

We are given the hypotenuse (15 m) and one of the legs (9 m).

Let's assign some values:

[tex]a=??\\c=15\\b=9[/tex]

Let's solve for b by using the Pythagorean Theorem.

[tex]a^2+b^2=c^2=\\a^2+9^2=15^2=\\a^2+81=225=\\a^2=144=\\a=12[/tex]

So, the length of the missing leg, a, is 12 m.

Answer:

The length of the missing leg is 12 m.

Step-by-step explanation:

SOLUTION :

Here we have given that the base of triangle is 9 m and hypotenuse is 15 m. We have to find the the height of triangle.

Using Pythagoras Theorem to find the height of triangle :

[tex]\quad{\longrightarrow{\sf{{(H)}^{2} = {(b)}^{2} + {(h)}^{2}}}}[/tex]

Substituting all the given values in the formula to find the height of triangle :

[tex]\quad{\longrightarrow{\sf{{(H)}^{2} = {(b)}^{2} + {(h)}^{2}}}}[/tex]

[tex]\quad{\longrightarrow{\sf{{(15)}^{2} = {(9)}^{2} + {(h)}^{2}}}}[/tex]

[tex]\quad{\longrightarrow{\sf{{(15 \times 15)} = {(9 \times 9)} + {(h)}^{2}}}}[/tex]

[tex]\quad{\longrightarrow{\sf{{(225)} = {(81)} + {(h)}^{2}}}}[/tex]

[tex]\quad{\longrightarrow{\sf{{(h)}^{2} = 225 - 81}}}[/tex]

[tex]\quad{\longrightarrow{\sf{{(h)}^{2} = 144}}}[/tex]

[tex]\quad{\longrightarrow{\sf{h = \sqrt{144}}}}[/tex]

[tex]\quad{\longrightarrow{\sf{\underline{\underline{\pink{h = 12 \: m}}}}}}[/tex]

Hence, the height of triangle is 12 m.

Answer:

B

Step-by-step explanation:

The overall mean number of hours worked can be determined by calculating the weighted average of the means for males and females, taking into account the sample size as weights.

Given:

X₁ = 6 (mean number of hours worked for males)

X₂ = 9 (mean number of hours worked for females)

n₁ = 30 (sample size for males)

n₂ = 20 (sample size for females)

The overall mean number of hours worked, denoted as X, can be calculated as follows:

X = (X₁ * n₁ + X₂ * n₂) / (n₁ + n₂)

Plugging in the given values:

X = (6 * 30 + 9 * 20) / (30 + 20)

X = (180 + 180) / 50

X = 360 / 50

X = 7.2

The average size of the 15 diameters is 25.00mm. Using the concept of percentages, the mass of copper, lead, and tin in the bronze bearing are 140 kg, 40 kg, and 20 kg, respectively.

To find the average size of the 15 diameters, we need to calculate the sum of all the dimensions and then divide by 15 (the total number of diameters).

The sum of the dimensions can be calculated as follows:

(5 x 24.99mm) + (6 x 25.01mm) + (4 x 25.00mm)

= 375.01mm

Now, we can calculate the average size by dividing the sum by 15:

Average size = 375.01mm / 15

= 25.00mm (rounded to 2 decimal places)

Therefore, the average size of the 15 diameters is 25.00mm.

b.

To find the mass of each metal, we need to determine how much of each metal is present in the bronze bearing. This can be done using the concept of percentage

Let's start by finding the mass of copper in the bearing:

Mass of copper = 70% of 200 kg = 0.7 x 200 kg = 140 kg

Next, let's find the mass of lead in the bearing:

Mass of lead = 20% of 200 kg = 0.2 x 200 kg = 40 kg

Finally, let's find the mass of tin in the bearing:

Mass of tin = 10% of 200 kg = 0.1 x 200 kg = 20 kg

Therefore, the mass of copper, lead, and tin in the bronze bearing are 140 kg, 40 kg, and 20 kg, respectively.

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When the top of the ladder is 16 feet above the ground, the foot of the ladder is moving away from the wall at a speed of approximately 3.86 feet per second.

This is a related rates problem involving a ladder leaning against a wall. Let's denote the distance of the foot of the ladder from the wall as x, and the height that the top of the ladder reaches as y. We are given that dy/dt = -2 ft/s (since the top is slipping down the wall) and we want to find dx/dt (the speed at which the foot of the ladder is moving away from the wall) when y = 16 ft.

Using the Pythagorean theorem, we have:

[tex]x^2 + y^2 = 17^2[/tex]

Differentiating implicitly with respect to time, we get:

[tex]2x(dx/dt) + 2y(dy/dt) = 0[/tex]

Substituting the given values, we get:

[tex]2x(dx/dt) + 2(16)(-2) = 0[/tex]

Simplifying, we get:

[tex]2x(dx/dt) = 64[/tex]

Dividing both sides by 2x, we get:

dx/dt = 64/(2x)

We know that y = 16, so we can use the Pythagorean theorem to solve for x:

[tex]x^2 + 16^2 = 17^2x^2 = 17^2 - 16^2x^2 = 33[/tex]

Taking the square root, we get:

[tex]x = sqrt(33)[/tex]

Substituting this into our expression for dx/dt, we get:

[tex]dx/dt = 64/(2*sqrt(33)) ≈ 3.86 ft/s[/tex]

Therefore, when the top of the ladder is 16 feet above the ground, the foot of the ladder is moving away from the wall at a speed of approximately 3.86 feet per second.

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If PQRS are points on a circle with the centre O, PS is a diameter of the circle Angle PQR=136, the measure of angle RPS is 88 degrees.

Since QR is parallel to PS, we can use alternate interior angles to determine that angle QPS is equal to angle PQR. This means that angle QPS is also 136 degrees.

Angle PQR and angle QPS both subtend the same arc, which is the arc between points P and R on the circle. Therefore, the two angles are equal.

We can use this fact to find the measure of angle RPS. First, we know that the sum of angles in a quadrilateral is 360 degrees. Therefore, we can find the measure of angle PSR as follows:

Angle PSR = 360 degrees - Angle PQR - Angle QPS

Angle PSR = 360 degrees - 136 degrees - 136 degrees

Angle PSR = 88 degrees

Next, we use the fact that angles at the circumference of a circle subtended by the same arc are equal. Angle PSR and angle RPS both subtend the same arc, which is the arc between points P and R on the circle. Therefore, the two angles are equal.

Angle RPS = Angle PSR = 88 degrees

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Complete question is:

PQRS are points on a circle with the centre O PS is a diameter of the circle Angle PQR=136 Work out the size of angle RPS

To save on shipping costs, Camile should choose a box that is lightweight and has a small volume.

This is because she has realized that she is charged based on the volume of the box and not the weight.

Therefore, a smaller volume box would cost her less than a larger volume box of the same weight.

For example, if Camile needs to ship a 5-pound item, she should choose a smaller box with a volume that is just enough to fit the item, rather than a larger box with more empty space. This is because the larger box would have a greater volume, and therefore, incur a higher shipping cost even though it weighs the same as the smaller box.

In summary, when selecting a box to save on shipping costs, it is important to consider both weight and volume. Camile should choose a box that is lightweight and has a smaller volume to reduce her shipping costs.

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Answer:

Step A: The third quartile is 9.5, choice d.

Step B: The median of the data set is 6.5.

Step C: The IQR of the data set is 6, and we found this value by subtracting the first quartile from the third quartile (9.5 - 3.5 = 6).

Step-by-step explanation:

First, let's analyze the data set.

1 2 3 4 5 6 7 8 9 10 11 12

Since this data set is already sorted in numerical order, we can determine the median by finding the middle value that divides the data set in half. With 12 values in the data set, the median would be between the 6th and 7th numbers, so we can find this by using the calculation (6+7)/2 = 6.5.

                 6.5

{1 2 3 4 5 6} | {7 8 9 10 11 12}

With this median, we split our data set into two halves. Now, we can find the first quartile, or the 25th percentile, by finding the median of the first half. This would be the value between 3 and 4, so (3+4)/2 = 3.5.

       3.5        6.5

{1 2 3} | {4 5 6} | {7 8 9 10 11 12}

We can repeat this step in the second half in order to find the third quartile or the 75th percentile. The median of the second half would be between 9 and 10, so (9+10)/2 = 9.5.

       3.5         6.5        9.5

{1 2 3} | {4 5 6} | {7 8 9} | {10 11 12}

Now we know Q1 (first quartile) and Q3 (third quartile), we can find the IQR which is Q3 - Q1, so Q3 - Q1 = 9.5 - 3.5 = 6.

So now we can answer the question:

Step A: The third quartile is 9.5, choice d.

Step B: The median of the data set is 6.5.

Step C: The IQR of the data set is 6, and we found this value by subtracting the first quartile from the third quartile (9.5 - 3.5 = 6).

C21 represents 4 senior boys.

A matrix, which is used to represent a mathematical object or an attribute of one, is a rectangular array or table containing numbers, symbols, or expressions that are organized in rows and columns. is a matrix having two rows and three columns, for instance

Given:

[tex]\left[\begin{array}{ccc}5&6\\4&3\\\end{array}\right][/tex], [tex]\left[\begin{array}{ccc}c11&c12\\c21&c22\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}Junior boy&Junior girl\\Senior boy&Senior girl\\\end{array}\right][/tex]

4 Senior boys is c21 represented.

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Answer:

1) She needs (35 × 2) + 8 = 78 inches

The survey found that 86% of 2006 US students in grades 10-12 agreed with the statement "if I make a mistake, I try to figure out where I went wrong." The survey's margin of error is +/- 3.7%, so we can be 95% confident the true proportion falls between 82.3% and 89.7%.

This means that we can be 95% confident that the true proportion of students who agree with the statement lies between 82.3% and 89.7%. This interval is calculated as follows

Subtract the margin of error from the sample proportion to get the lower bound: 86% - 3.7% = 82.3%

Add the margin of error to the sample proportion to get the upper bound: 86% + 3.7% = 89.7%

So, we can say with 95% confidence that the true proportion of students who agree with the statement is somewhere between 82.3% and 89.7%.

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Answer:

20/8 or 20:8

Step-by-step explanation:

Ok, so we start off with a smaller square with one side being 8.

We then have to go from one side being 8 to one side being 20.

So, the ratio has to be a number larger than 1 to go from smaller to larger, so we can use the ratio of 20/8 (or 2.5).

Check:

2.5x8=20

11/8 cup of the bowl is made up of granola..

What is fraction?

A fraction represents a part of a whole, and it is written in the form of one integer written above another, separated by a horizontal line. The integer on top is called the numerator, and the integer on the bottom is called the denominator.

The numerator represents the number of parts being considered, while the denominator represents the total number of equal parts that make up the whole. For example, the fraction 3/4 represents three parts out of a total of four equal parts.

Fractions can be used to represent values that are not whole numbers, such as halves, thirds, quarters, etc. They are commonly used in everyday life, such as when measuring ingredients in cooking, dividing up a pizza or a cake, or expressing a probability.

To find the amount of granola in the bowl, we need to subtract the total amount of yogurt and blueberries from the total volume of the bowl.

First, let's add up the yogurt and blueberries:

7/8 cup Greek yogurt + 1 1/4 cup blueberries

= 7/8 + 5/4 (we need to find a common denominator)

= 14/16 + 20/16

= 34/16

Next, let's convert the total volume of the bowl to a fraction with a common denominator of 16:

3 1/2 = 7/2 = 56/16

Now we can find the amount of granola:

Amount of granola = Total volume of bowl - Amount of yogurt - Amount of blueberries

= 56/16 - 34/16

= 22/16

Simplifying the fraction, we get:

Amount of granola = 11/8

Therefore, 11/8 cup of the bowl is made up of granola.

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The length of JL is 20.572.

An angle is a geometric figure formed by two rays or lines that share a common endpoint, called the vertex of the angle. Angles are measured in degrees or radians, and they are used to describe the relationships between lines and shapes in geometry.

The size of an angle is determined by the amount of rotation needed to bring one of the rays into coincidence with the other. A full rotation around the vertex is equivalent to 360 degrees or 2π radians. A right angle, which is formed by one ray perpendicular to another, has a measure of 90 degrees or π/2 radians.

Angles can be classified according to their measures as acute angles (less than 90 degrees), right angles (exactly 90 degrees), obtuse angles (between 90 and 180 degrees), straight angles (exactly 180 degrees), and reflex angles (between 180 and 360 degrees).

Angles also have a number of important properties and relationships, such as vertical angles (formed by two intersecting lines and are congruent), complementary angles (two angles whose measures sum up to 90 degrees), and supplementary angles (two angles whose measures sum up to 180 degrees).

cos  A= (leg adjacent to ∠A)/hypotenuse: cos(∠KLM)= [tex]\frac{LM}{KL}[/tex]

Substitute, LM= 7, KL= 12 : cos(∠KLM)= [tex]\frac{7}{12}[/tex]

Calculate cos(∠KLM)= [tex]\frac{7}{12}[/tex] : ∠KLM= 54.315°

Representing same angles: ∠JLK= ∠KLM

Substitute ∠KLM= 54.315° into ∠JLK= ∠KLM ⇒∠JLK= 54.315°

cos  A= (leg adjacent to ∠A)/hypotenuse: cos(∠JLK)=[tex]\frac{KL}{JL}[/tex]

Substitute, KL= 12, ∠JLK= 54.315°  ⇒ cos(∠JLK)= [tex]\frac{12}{JL}[/tex]

Calculate cos(54.315°)=[tex]\frac{12}{JL}[/tex] ⇒ JL= 20.572

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The complete question is:

The total surface area to paint is 22000 sq. ft.

Surface area is the measurement of the outer surface of an object. It is often used to calculate the area of a three-dimensional object, such as a cube, cylinder, or sphere, and is also used to calculate the area of the faces of a solid object. Surface area is measured in square units such as square centimeters (cm2), square meters (m2), or square inches (in2).

Surface Area = 2(lw + lh + wh)

Surface Area = 2((100' x 50') + (100' x 40') + (50' x 40'))

Surface Area = 2(5000' + 4000' + 2000')

Surface Area = 2(11000')

Surface Area = 22000 sq. ft.

Answer: The total surface area to paint is 22000 sq. ft.

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Answer:

2200

Step-by-step explanation:

The common ratio is -1/3 and the initial term is -4, then the formula is:

A(n) = -4*(-1/3)^(n - 1)

Remember that in a geometric sequence, to get the next term we need to multiply the previous term by the common ratio.

To get the common ratio, take the quotient between two consecutive terms.

We will get:

(4/3)/(-4) = -1/3

Then the n-th term of the geometric sequence is:

A(n) = -4*(-1/3)^(n - 1)

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Answer:

[tex](-4)\left(\frac{1}{3}\right)^{n-1}[/tex]

Step-by-step explanation:

The common ratio between any two terms in a geometric sequence is constant. Let this ratio be denoted by r. Then, we have:

[tex]r = \frac{\frac{4}{3}}{-4} = \frac{-\frac{4}{9}}{\frac{4}{3}} = \frac{\frac{4}{27}}{-\frac{4}{9}} = \frac{1}{3}[/tex]

Using this value of r, we can write the formula for the nth term an as:

[tex]an=[/tex][tex](-4)\left(\frac{1}{3}\right)^{n-1}[/tex]

Answer:

49.60

Step-by-step explanation:

she saves 12.40

answer is : x 25. y = 20 both y's will cancel . 2x =50.=x=25

a).The bearing of point A from B is 234°.

b). The bearing of point B from point A is 054°.

Bearing is usually measured in degrees, with 0° indicating the reference direction (usually North), and increasing clockwise to 360°. It refers to the direction or angle between a reference direction and a point or object.

The bearing of point A from B is the angle measured from the north of B to the straight line distance between A and B which is 234°. While the bearing of point B from point A is the angle measure starting from the north of A to the straight line distance between A and B which is 054°.

Therefore, the bearing of point A from B is 234° while the bearing of point B from point A is 054°.

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The documentation provided with the procedure states that the procedure will display the value of (x + y) / x.

This means that the result of the calculation will be shown to the user, and it will be the value obtained by adding x and y, then dividing the result by x.

However, the documentation also includes a very important requirement for the parameter x: it must not be 0. This is because dividing by zero is not a valid mathematical operation, and will result in an error. Therefore, it is crucial to ensure that the value of x passed to the procedure is a non-zero integer.

To summarize, the "calculate" procedure takes two integer parameters, x and y, and displays the value of (x + y) / x.

It is important to note that the value of x must not be 0, as dividing by zero is not a valid mathematical operation.

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Buddy's answer of 19 feet for the maximum height of his punt is correct, based on the given quadratic function.

How to solve the question?

To determine the maximum height of the punt, we need to find the vertex of the parabolic function h(x) = −.02x² + 1.2x + 4, which represents the height of the football at any given horizontal distance x from the point of impact.

The vertex of a parabola in the form y = ax² + bx + c can be found using the formula x = -b / 2a, which gives the x-coordinate of the vertex, and then substituting that value into the function to find the corresponding y-coordinate.

In this case, we have a = -.02, b = 1.2, and c = 4. So the x-coordinate of the vertex is x = -b / 2a = -1.2 / (2*(-.02)) = 30, and the corresponding maximum height is h(30) = -.02(30)2 + 1.2(30) + 4 = 19 feet.

Therefore, Buddy's answer of 19 feet for the maximum height of his punt is correct, based on the given quadratic function.

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In the event of shortening the standard error of mean to 15 we have to increase the size to 400. Therefore, the correct answer is Option B.

The  given standard error of the mean for a sample of 100 is 30. So to cut the standard error of the mean to 15, we have to proceed by increasing the sample size to 400.

The  formula for evaluating the standard error of mean
SEM = SD / √(n)
here, SEM = standard error of the mean,
SD = standard deviation
n = sample size
Staging the values
15 = SD / √(100)
15 x √(100) = SD
SD = 150
Now evaluating for the value of n
15 = 150 / √(n)
15 x √(n) = 150
√(n) = 10
n = 100
Now looking at the formula, we need to decrease SEM by half,

So we proceed by increasing the  sample size by a factor of 4.

In the event of shortening the standard error of mean to 15 we have to increase the size to 400. Therefore, the correct answer is Option B.

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Answer:

Step-by-step explanation:

I do believe you should most definitly add units

Answer:

x = -3

Step-by-step explanation:

[tex]-4x-5-11x=40\\-15x=40+5[/tex]

[tex]x=\frac{45}{-15}[/tex]

[tex]x=-3[/tex]

Hope this helps.

95% confidence that the population mean is less than 6 minutes since the upper limit of the confidence interval is below 6 minutes.

95% confidence that the population mean is within the range of 4.897 to 5.763 minutes.

The t-based 95 percent confidence interval for the population mean:

CI =[tex]\bar x\pm t\alpha/2 \times (s/\sqrt n)[/tex]

[tex]\bar x[/tex]  is the sample mean, s is the sample standard deviation, n is the sample size, tα=/2 is the t-value corresponding to the desired level of confidence and (s/√n) is the standard error of the mean.

The sample size is 100, the sample mean is 5.33, and the sample standard deviation is 2.207, the standard error of the mean is:

s/√n

= 2.207/√100

= 0.221

The t-value corresponding to a 95% confidence level with 99 degrees of freedom (100 - 1), look it up in a t-distribution table or use a calculator.

The t-value is approximately 1.984.

The 95% confidence interval for the population mean is:

CI = 5.33 ± 1.984 × 0.221

= [4.897, 5.763]

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The correct statement regarding the best measure of center for the data-set in this problem is given as follows:

The mean is the best measure of center because there are no outliers present.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

The dot plot shows the number of times that each observation appears, hence the data-set is given as follows:

2, 3, 3, 3, 4, 6, 6, 7, 7, 8, 9.

We can see that the data-set is clustered, meaning that there are no outliers, hence the mean can be used instead of the median.

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The odds of rolling two 6-sided dice and getting a total between the two dice that is a multiple of three are approximately 31%.

To determine the odds of rolling two 6-sided dice and getting a total between the two dice that is a multiple of three,

we first need to identify the possible outcomes. The possible sums of rolling two dice range from 2 to 12. We then need

to find the multiples of three within that range, which are 3, 6, 9, and 12.

Next, we need to find the number of ways that we can roll each of these multiples of three. To do this, we can create a

chart:
Sum | Ways to roll
---|---
3 | 1
6 | 5
9 | 4
12 | 1

So there are a total of 11 ways to roll a multiple of three with two dice.

To find the odds, we need to divide the number of favorable outcomes (11) by the total number of possible outcomes

when rolling two dice (36), and then convert the fraction to a percentage or a ratio.

11/36 = 0.3056 or approximately 31%

Therefore, the odds of rolling two 6-sided dice and getting a total between the two dice that is a multiple of three are approximately 31%.

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Answer:

The surface area (SA) formula for a rectangular prism is:

SA = 2lw + 2lh + 2wh

where l is the length, w is the width, and h is the height.

For the cereal box object given, we have:

l = 12 inches

w = 8 inches

h = 1.75 inches

So, substituting these values into the formula, we get:

SA = 2(12)(8) + 2(12)(1.75) + 2(8)(1.75)

SA = 192 + 42 + 28

SA = 262 square inches

Therefore, the surface area of the rectangular prism cereal box is 262 square inches.

Step-by-step explanation:

The SURFACE AREA OF THE RECTANGULAR PRISM is 262 in²

SURFACE AREA (S.A) OF RECTANGULAR PRISM= 2lw+2lh+2wh

LENGTH=12 inches

WIDTH= 8 inches

HEIGHT=1.75 inches



Applying the formula

We get

S.A=2*(12*8)+2*(12*1.75)+2*9(8*1.75)

S.A = 192+42+28 sq inches

S.A= 262 sq inches