(6y + 10) - (2y + 3)

The diameter of the circle is 8 cm, and its area is approximately 50.27 cm².

Tito draws a square with side lengths of 8 cm.

He inscribes a circle inside the square so that it touches all four sides.

Diameter and area of the circle:
The diameter of the circle is equal to the side length of the square, since the circle touches all four sides of the square.
Diameter = 8 cm
Calculate the radius of the circle by dividing the diameter by 2.
Radius = Diameter ÷ 2 = 8 cm ÷ 2 = 4 cm
Calculate the area of the circle using the formula:

Area = π × (Radius)².
Area = π × (4 cm)² = π × 16 cm² ≈ 50.27 cm².

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Question: The largest square that can be drawn in a circle has a side whose length is 0.707 times the diameter of the circle. By this rule, find the length of the side of such a square when the diameter of the circle is(a) 14.35 cm (b) 8.63 cm

Answer:

1320

Step-by-step explanation:

Use the formula for sum of series, s(a) = n/2(2a + (n-1)d)

The terms increase by 6, so d is 6

a is the first term, -56

n is the terms you want to find, 33

Plug in the numbers, 33/2 (2(-56)+(32)6)

Simplify into 33(80)/2 and you get 1320

Answer: 5 + a = t

Step-by-step explanation:

She fed her five in the morning,  the a is a variable representing the amount she fed in the afternoon, and the t is a variable representing the total amount of apple chunks fed. Because we do not know how many chunks she fed him these two values have to be variables.

To solve the given problems, we'll use the properties of the normal distribution with mean μ = 100 and standard deviation σ = 10.

a. Probability that X > 85:

To find this probability, we need to calculate the area under the normal curve to the right of 85. We can use the standard normal distribution table or a calculator to find the corresponding z-score and then use the z-table to find the probability.

First, let's calculate the z-score:

z = (X - μ) / σ

z = (85 - 100) / 10

z = -15 / 10

z = -1.5

Using the z-table or a calculator, we find that the probability of Z > -1.5 is approximately 0.9332.

Therefore, the probability that X > 85 is 0.9332 (rounded to four decimal places).

b. Probability that X < 80:

Similarly, we'll calculate the z-score for X = 80:

z = (X - μ) / σ

z = (80 - 100) / 10

z = -20 / 10

z = -2

Using the z-table or a calculator, we find that the probability of Z < -2 is approximately 0.0228.

Therefore, the probability that X < 80 is 0.0228 (rounded to four decimal places).

c. Probability that X < 90 or X > 130:

To calculate this probability, we'll find the individual probabilities of X < 90 and X > 130, and then subtract the probability of their intersection.

For X < 90:

z = (90 - 100) / 10

z = -10 / 10

z = -1

Using the z-table or a calculator, we find that the probability of Z < -1 is approximately 0.1587.

For X > 130:

z = (130 - 100) / 10

z = 30 / 10

z = 3

Using the z-table or a calculator, we find that the probability of Z > 3 is approximately 0.0013.

Since these events are mutually exclusive, we can add their probabilities:

P(X < 90 or X > 130) = P(X < 90) + P(X > 130)

P(X < 90 or X > 130) = 0.1587 + 0.0013

P(X < 90 or X > 130) = 0.1600

Therefore, the probability that X < 90 or X > 130 is 0.1600 (rounded to four decimal places).

d. 99% of the values are between what two X-values (symmetrically distributed around the mean)?

To find the two X-values, we need to find the corresponding z-scores for the cumulative probabilities of 0.005 and 0.995. These probabilities correspond to the tails beyond the 99% range.

For the left tail:

z = invNorm(0.005)

z ≈ -2.576

For the right tail:

z = invNorm(0.995)

z ≈ 2.576

Now we can find the corresponding X-values:

X1 = μ + z1 * σ

X1 = 100 + (-2.576) * 10

X1 = 100 - 25.76

X1 ≈ 74.24

X2 = μ + z2 * σ

X2 = 100 + 2.576 * 10

X2 = 100 + 25.76

X2 ≈ 125.76

Therefore, 99% of the values are greater than 74.24 and less than 125.76 (rounded to two decimal places).

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Answer:

Step-by-step explanation:

Use the slope formula.

Slope formula:

\(\Longrightarrow: \sf{\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{RISE}{RUN} }\)

\(\sf{y_2=9}\\\\\sf{y_1=6}\\\\\sf{x_2=10}\\\\\sf{x_1=3}\)

Solution: Rewrite it down.

\(\sf{\dfrac{9-6}{10-3}=\boxed{\sf{\dfrac{3}{7}}}\)

I hope this helps! Let me know if you have any questions.

Answer:

true

Step-by-step explanation:

Answer:

false because 140.23 is not less then 140.203

the dimensions of the lot is 100 yards by 400 yards. In this problem, a parking lot has a rectangular area of 40,000 square yards, and the length is 200 yards more than twice the width.

Determining the dimensions of a rectangular area, such as a parking lot, can be a useful task for many purposes, such as planning and designing a new lot or estimating the amount of space available for parking.

Let's call the width of the parking lot "w". Then, the length of the parking lot can be represented as 2w + 200.

The total area of the parking lot is 40,000 square yards, so we can set up an equation to solve for w: w * (2w + 200) = 40,000.

Solving for w, we get w = 100. This means that the width of the parking lot is 100 yards and the length is 2 * 100 + 200 = 400 yards.

The dimensions of the parking lot are 100 yards by 400 yards.

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Answer:

......................

Step-by-step explanation:

......................

Answer:

4(3x-5)=-80

12x-20=-80

12x =-80+20

12x= -60

X= -60/12

X=-5

Step-by-step explanation:

Answer:

x = -5

Step-by-step explanation:

4(3x – 5) = -80

Divide each side by 4

4/4(3x – 5) = -80/4

3x-5 = -20

Add 5 to each side

3x-5+5 = -20+5

3x = -15

Divide by 3

3x/3 = -15/3

x = -5

The other two sides each have a maximum length of 14 centimeters.

The square of the longest side of an obtuse triangle is greater than the sum of the squares of the other two sides. As a result, the equal legs must have a length L such that \(L^{2}\) + \(L^{2}\) = 2 \(L^{2}\) is less than \(( 20 cm )^{2}\) = 400 \(cm^{2}\). The maximum whole number L that works is 14 cm.

An obtuse-angled triangle is one that has one of its interior angles that is greater than 90°. If one of the angles in an obtuse triangle is greater than 90°, the sum of the remaining two angles is less than 90°. A triangle is called an obtuse-angled triangle or obtuse triangle if any of its angles is an obtuse angle or greater than 90°. The interior angles of the obtuse triangle add up to only 180°. When two shapes have the same shape and size, they are congruent. If two figures are congruent, then their mirror images are the same. Two segments are congruent if their measurements are the same.

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Question :

The longest side of an isosceles obtuse triangle measures 20 centimeters. The other two side lengths are congruent but unknown. What is the greatest possible whole-number value of the congruent side lengths?

The z-score of an appliance that stopped working at 64 months is 2.

z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

\(z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean,\sigma=standard\ deviation\\\)

Given that:

mean = 48, standard deviation = 8 months

For x = 64 months:

\(z=\frac{64-48}{8} \\\\z=2\)

The z-score of an appliance that stopped working at 64 months is 2.

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Answer:

D, 2

Step-by-step explanation:

edge

Answer:

The answer is B and C.

Answer: B AND C

Step-by-step explanation:

Remote interior angles are angles that are opposite from the exterior angles (5 in this case).

Answer:

\(\frac{-1}{2}ab^{12}\)

\(\frac{w^{10}}{3y^4}\)

Step-by-step explanation:

Given the expression;

\(\frac{-2a^2b^4}{4ab^{-8}}\\= \frac{-2}{4}*a^{2-1}b^{4-(-8)}\\= \frac{-1}{2}ab^{12}\)

Similarly for the expression;

\(\frac{-5w^4y^{-2}}{-15w^{-6}y^2}\\= \frac{-5}{-15}*w^{4-(-6)}y^{-2-2}\\= \frac{1}{3}w^{10}y^{-4} \\= \frac{w^{10}}{3y^4}\)

The answer is x=−4 and y=−3

The probability of the temperature never exceeding 122 F is very low, while the probability of it remaining within a narrow range of 118 F to 120 F is virtually zero.

a) To find the probability that the temperature never exceeds 122 F, we need to calculate the z-score of 122 F using the formula z = (x - mean) / standard deviation. This gives us a z-score of -0.97. We can then use a standard normal distribution table or calculator to find the probability of a z-score less than or equal to -0.97, which is 0.0004.

b) To find the probability that the temperature remains within 118 F and 120 F, we need to calculate the z-scores of both values using the same formula as above. The z-score of 118 F is -1.87 and the z-score of 120 F is -1.16. We can then use a standard normal distribution table or calculator to find the probability of a z-score between -1.87 and -1.16, which is approximately zero.

c) To find how many standard deviations away from the mean a given temperature of 95 F is, we need to calculate the z-score using the same formula as above. The z-score of 95 F is -9.29, which means it is 9.29 standard deviations below the mean.

d) To find the temperature that is 1.8 standard deviations below the mean, we need to use the formula x = mean - z * standard deviation, where x is the desired temperature, mean is 123.8 F, z is 1.8, and standard deviation is 3.1 F. This gives us a temperature of 118.7 F.

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Every mile traveled along the stream, the elevation changes by 50 feet/mile.

The gradient of the stream can be calculated by dividing the elevation change by the distance traveled. In this case, the stream has an elevation change of 100 feet over a distance of 2 miles. Thus, the gradient can be calculated as:

Gradient = Elevation change / Distance traveled

= 100 feet / 2 miles

= 50 feet/mile

The gradient is an important concept in many fields, including geology, hydrology, and civil engineering. It represents the rate at which a physical quantity, such as elevation or temperature, changes with distance. A steep gradient indicates a rapid change, while a gentle gradient indicates a slow change.

Therefore, the answer is option (a) 50 feet/mile. This means that for every mile traveled along the stream, the elevation changes by 50 feet.

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Answer:

126 students

Step-by-step explanation:

18+2=20

140 divided by 20=7

7x18=126

140-126=14 chaperones

The primary tool or measure for determining whether the assumed regression model is appropriate is the residual plot.

A residual plot is a graph that shows the residuals, or the differences between the observed values and the predicted values from the regression model, plotted against the predictor variable(s). If the residuals are randomly scattered around zero, with no discernible pattern, then the regression model is a good fit for the data.

However, if there is a pattern in the residuals, such as a curved or U-shaped relationship, then the regression model may not be appropriate and a different model may need to be considered.

In addition to the residual plot, other measures such as the coefficient of determination (R-squared), the p-values of the regression coefficients, and the normality of the residuals can also be used to evaluate the goodness of fit of a regression model.

However, the residual plot is often considered the primary tool for assessing the adequacy of a regression model.

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Taking into account the least-squares regression line ln(element)=2.304-0.101(time). 1.496 grams of an unstable element will still be present after 8 years.

Given that,

Taking into account the least-squares regression line ln(element)=2.304-0.101(time).

We have to find how many grams of an unstable element will still be present after 8 years.

The equation is ln(elements)=2.304-0.101(time) with the element and time.

ln is nothing but a natural logarithm.

So,

We substitute 8 years in place of time.

ln(element)=2.304-0.101(time).

ln(element)=2.304-0.101(8)

ln(element)=2.304-0.808

ln(element)=1.496

Therefore, 1.496 grams of an unstable element will still be present after 8 years.

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Answer: badkid jay

Step-by-step explanation: because he gets him everything he ask for and shows favoritism towards him

Answer:

Step-by-step explanation:

PennyWise

NickleSmart

DimeSharp

QuarterIntelligent

The percent of the class will be attending the field trip is 75%.

If one-fourth of Jody's class cannot attend the upcoming field trip, it means that three-fourths (or 75%) of the class will be able to attend. To determine this, we can divide the whole class into four equal parts, with each part representing one-fourth of the class.

Since one-fourth of the class cannot attend, we subtract this portion from the whole class. As a result, three-fourths of the class remains, which represents the percentage of students attending the field trip.

To calculate the percentage, we multiply the fraction by 100. Therefore, 75% of the class will be attending the field trip.

Mathematically, the calculation can be expressed as follows:

3/4 * 100 = 75%

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The midpoint of the midsegment of Trapezoid is   E(2m, 2n) and F (2(q+p), 2n).

According to the question,

The vertices of the trapezoid are A(4m , 4n) , B(4q , 4n) , C(4p , 0) and D(0,0).

Let mid-point of midsegment of Trapezoid be E and F

Using section formula

E (x- coordinate)= 1*4m + 0 /2

E (x- coordinate)=2m

E (Y- coordinate)= 4n/2

E  (Y- coordinate)=2n

So, the coordinates of E (2m, 2n)

similarly,

F (x- coordinate)= (1*4q + 1*4p)/2

F (x- coordinate)=2(p + q)

F (Y- coordinate)= 4n/2

F(Y- coordinate)=2n

So, the coordinates of F (2(q +p), 2n)

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Answer:

A, C

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

To find the points for each question, you must divide the number of points (200) by the number of questions (40) to get the number of points for each question

\(\frac{200}{40}\)

Divide 200 by 40 to get

\(\frac{5}{1}\) or \(5\)

Hope this helps. If you have any follow-up questions, feel free to ask.

Have a great day!

Answer:

5 points

Step-by-step explanation:

200points / 40 questions = 5points/1question

then:

1 questión worths 5 points

All the missing angles of the triangles are;

m∠1 =  50°

m∠4 = m∠2 = 30°

m∠3 = 50°

m∠5 = 40°

m∠6 = 50°

m∠7 = 90°

We know that the sum of angles in a triangle is 180 degrees. Thus;

m∠1 = 180 - (90 + 40)

m∠1 =  50°

We know that sum of angles on a straight line is 180 degrees. Thus;

m∠4 = m∠2 = 180 - 50

m∠4 = m∠2 = 30°

Now, opposite angles are equal and as such;

m∠1 =  m∠3 = 50°

Using the first concept, we can say that;

m∠5 = 180 - (90 + 50)

m∠5 = 40°

Similarly,

m∠6 = 90 - 40

m∠6 = 50°

Similarly,

m∠7 = 90°

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a) The equation of the regression Line is; y = -1.189 +  0.0021x

b) What the y-intercept of the regression line indicates is that regression line is only in the area with y > 0.

c) The slope of the regression line predicts an increase of 0.0021 in GPA score.

d)  The GPA of a freshman who scored a combined 1400 is; 1.751

e) The SAT scores are effective in predicting academic success during the first semester of the freshman year at this college.

f) Positive

a) Let SAT be represented as x and let GPA be represented as y.

Now, formula for Covariance is;

Covariance = r(s_x * s_y)

We are given;

correlation; r = 0.47

s_x = 123

s_y = 0.56

Cov = 0.47 * 123 * 0.56 = 20.81

Now, the equation is;

y = B₀ + B₁x

Where;

B₁ = cov/var(x) = cov/sₓ²

B₁ = 20.81/(123 * 123)

B₁ = 0.0021

B₀ = 2.66 - (1.833 * 0.0021)

B₀ = -1.189

Thus, the equation is;

y = -1.189 +  0.0021x

b) GPA can't be negative. So it is a meaningless value. Thus, the regression line is only in the area with y > 0.

c) For each additional SAT score, the model predicts an increase of 0.0021 in GPA score.

d) To predict the GPA of a freshman who scored a combined 1400, it is the formula;

y(1400) = −1.189 + (0.0021 * 1400)

y(1400) = 1.751

e) r² = 0.472

r = 0.2209.

SAT scores is not an effective predictor of college GPA, There are only 22.09% of variability in GPA can be explained by the model.

f) Positive, it means GPA is higher than model predicts

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Answer:

The side lengths of the larger polygon are;

15 cm

20.625 cm

16.875 cm

9.375 cm

13.125 cm

Step-by-step explanation:

Firstly, we need to calculate the perimeter of the first polygon

Mathematically, we can get this by adding the side lengths together

We have this as;

5 + 7 + 8 + 11 + 9

= 40 cm

so we have the ratio of the lengths of both as;

75 cm/40 cm = 1.875

Now, we simply will multiply the lengths of the smaller polygon by 1.875

So we have the side lengths of the bigger polygon as;

1.875 * 5 = 9.375 cm

1.875 * 7 = 13.125 cm

1.875 * 8 = 15 cm

1.875 * 9 = 16.875 cm

1.875 * 11 = 20.625 cm

Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

c

Step-by-step explanation: