the equation of a vertical line passing through the point (-1,8) is
• x=1
• y=8
• y=1
• x=1

answer: 10

step by step explanation:

this is not a textbook way but

4:5 means 4/5 and we know that the numbers will be equal to this number so we can multiply the number 4/5*2/2 so we will get 8/10

8/10=4/5

and 8*10=80

so 1st no. is 8 and 2nd is 10

10>8

Answer:

greater number is 10

Step-by-step explanation:

the ratio of the 2 numbers = 4 : 5 = 4x : 5x ( x is a multiplier )

their product is 80 , that is

4x × 5x = 80

20x² = 80 ( divide both sides by 20 )

x² = 4 ( take square root of both sides )

x = \(\sqrt{4}\) = 2

then greater number = 5x = 5 × 2 = 10

Answer:

I do not understand the question

According to the first scale, 2 red balls = 1 star.

According to the second scale, 2 triangles = 1 star

So,

1 triangle = 1 red ball

1 star = 2 red balls

1 red ball = 1 red ball

Therefore, 2 + 1 + 1 = 4 red balls

The last scale needs 4 red balls

Given:

z be inversely proportional to the cube root of y.

When y =0.064, then z =3.

To find:

a) The constant of proportionality k.

b) The value of z when y = 0.125.​

Solution:

a) It is given that, z be inversely proportional to the cube root of y.

\(z\propto \dfrac{1}{\sqrt[3]{y}}\)

\(z=k\dfrac{1}{\sqrt[3]{y}}\)              ...(i)

Where, k is the constant of proportionality.

We have, z=3 when y=0.064. Putting these values in (i), we get

\(3=k\dfrac{1}{\sqrt[3]{0.064}}\)

\(3=k\dfrac{1}{0.4}\)

\(3\times 0.4=k\)

\(1.2=k\)

Therefore, the constant of proportionality is \(k=1.2\).

b) From part (a), we have \(k=1.2\).

Substituting \(k=1.2\) in (i), we get

\(z=1.2\dfrac{1}{\sqrt[3]{y}}\)

We need to find the value of z when y = 0.125.​ Putting y=0.125, we get

\(z=1.2\dfrac{1}{\sqrt[3]{0.125}}\)

\(z=\dfrac{1.2}{0.5}\)

\(z=2.4\)

Therefore, the value of z when y = 0.125 is 2.4.

Proportional quantities are either inversely or directly proportional. For the given relation between y and z, we have:

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

\(p = kq\)

where k is some constant number called constant of proportionality.

This directly proportional relationship between p and q is written as

\(p \propto q\)  where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n are two variables.

Then m and n are said to be inversely proportional to each other if

\(m = \dfrac{c}{n}\)

or

\(n = \dfrac{c}{m}\)

(both are equal)

where c is a constant number called constant of proportionality.

This inversely proportional relationship is denoted by

\(m \propto \dfrac{1}{n}\\\\or\\\\n \propto \dfrac{1}{m}\)

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

For the given case, it is given that:

\(z \propto \dfrac{1}{^3\sqrt{y}}\)

Let the constant of proportionality be k, then we have:

\(z = \dfrac{k}{^3\sqrt{y}}\)

It is given that when y = 0.064, z = 3, thus, putting these value in equation obtained above, we get:

\(k = \: \: ^3\sqrt{y} \times z = (0.064)^{1/3} \times (3) = 0.4 \times 3 = 1.2\)

Thus,  the constant of proportionality k is 1.2. And the relation between z and y is:

\(z = \dfrac{1.2}{^3\sqrt{y}}\)

Putting value y = 0.0125, we get:

\(z = \dfrac{1.2}{^3\sqrt{y}}\\\\z = \dfrac{1.2}{(0.125)^{1/3} } = \dfrac{1.2}{0.5} = 2.4\)

Thus, for the given relation between y and z, we have:

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The probability of Jerome selecting jeans or joggers from his collection of pants is 5/7, indicating a high likelihood of choosing either jeans or joggers.

Jerome has a total of 3 pairs of jeans and 2 pairs of joggers. Since the question asks for the probability of selecting jeans or joggers, we need to consider the favorable outcomes, which are the jeans and joggers, and the total number of possible outcomes, which is the total number of pants.

The total number of pants Jerome has is 3 (jeans) + 2 (joggers) + 1 (black pants) + 1 (khaki pants) = 7. Out of these 7 pants, the favorable outcomes are the jeans and joggers, which total 3 (jeans) + 2 (joggers) = 5.

Therefore, the probability of Jerome selecting jeans or joggers can be calculated as the favorable outcomes divided by the total number of outcomes: P(jeans or joggers) = 5/7.

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λ (lambda) is a variable in mathematics used to represent an unknown quantity or a function. It is typically used in calculus and algebra to denote the slope of a function or to express rates of change.

In mathematics, the symbol λ (lambda) is often used to represent various concepts depending on the context. In calculus, it is often used as a parameter in functions, particularly in optimization problems, where it can represent a Lagrange multiplier or a scaling factor. In linear algebra, λ is often used to denote an eigenvalue, which is a scalar quantity associated with a square matrix that represents how a transformation changes a vector.

In statistics, λ is often used to represent the rate parameter in the Poisson distribution, which models the probability of a certain number of events occurring in a given time interval. The meaning of λ varies depending on the specific branch of mathematics in which it is being used.

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The total value in cents of all coins in the any row would be 16 cents.

In the pattern you described, the coins are arranged in rows such that each subsequent row has one more coin than the previous row. Let's analyze the values of the coins to determine the total value in cents of all the coins in the th row.

Assuming the values of the coins are as follows:

Penny: 1 cent

Nickel: 5 cents

Dime: 10 cents

We can observe that the pattern repeats after every three coins. The first three coins in the pattern are penny, nickel, dime. These coins have a total value of 1 + 5 + 10 = 16 cents.

For the subsequent rows, the pattern repeats with an offset of 3. For example, in the fourth row, the coins are penny, nickel, dime, which have the same total value as the first row, i.e., 16 cents.

So, regardless of the value of "th" (the row number), the total value in cents of all the coins in that row will always be 16 cents.

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Answer:

78.8

Step-by-step explanation:

Answer:

2.75

Step-by-step explanation:

9.25-6.5=2.75

Answer:

4,000 is that answer to 3,623 to the nearest thousands.

Step-by-step explanation:

Answer:

alpha=cos^-1(0.6)

alpha=53°

sin(37+53)

=1

Answer:

Step-by-step explanation:

Since both sin θ and cos α have same value of 3/5 and both angles are in the I quadrant, the angles θ and α are complementary.

It means:

Answer:

18cm

Step-by-step explanation:

The solution to the inequality 4 ≤ -3x - 1 ≤ 9 is -5/3 ≥ x ≥ -10/3.

Given the inequality in the question;

4 ≤ -3x - 1 ≤ 9

To solve, first move all terms not containing x from center section of the inequality.

4 ≤ -3x - 1 ≤ 9

Add 1 to each sides of the inequality

4 + 1 ≤ -3x - 1 + 1 ≤ 9 + 1

4 + 1 ≤ -3x ≤ 9 + 1

Add 4 and 1

5 ≤ -3x ≤ 9 + 1

Add 9 and 1

5 ≤ -3x ≤ 10

Now, divide each term in the inequality by -3

5 / -3 ≥ -3x / -3 ≥ 10 / -3

Simplify

5 / -3 ≥ x ≥ 10 / -3

-5/3 ≥ x ≥ -10/3

Therefore, the solution is -5/3 ≥ x ≥ -10/3.

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The expression to determine the distance between the lowest and the highest point is -

{x} = 14505 + |- 282|

Given is a diagram that shows several planes, lines, and points.

The correct statement with respect to line {h} is -

Line h has points on planes R, P, and T.

Therefore, line {h} has points on planes {R}, {P} and {T} is the correct alternative.

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Answer:

1.3 < x < 37.7

Step-by-step explanation:

Given 2 sides of a triangle then the 3rd side x is in the interval

difference of 2 sides < x < sum of 2 sides , that is

19.5 - 18.2 < x < 19.5 + 18.2 , then

1.3 < x < 37.7

To find the displacement and total distance traveled by the object from t=0 to t=6, we need to integrate the velocity function over the given time interval.

The displacement can be found by integrating the velocity function v(t) with respect to t over the interval [0, 6]. The integral of v(t) represents the net change in position of the object during this time interval.

The total distance traveled can be determined by considering the absolute value of the velocity function over the interval [0, 6]. This accounts for both the forward and backward movements of the object.

Now, let's calculate the displacement and total distance traveled using the given velocity function v(t) = t^2 - (1/t) - 12 over the interval [0, 6].

To find the displacement, we integrate the velocity function as follows:

Displacement = ∫[0,6] (t^2 - (1/t) - 12) dt.

To find the total distance traveled, we integrate the absolute value of the velocity function as follows:

Total distance = ∫[0,6] |t^2 - (1/t) - 12| dt.

By evaluating these integrals, we can determine the displacement and total distance traveled by the object from t=0 to t=6.

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Answer:

87cm

Step-by-step explanation:

5*10=50

3*10=30

2.5*6=15-(5+3)=7

50+30+7=87cm

The flux of the vector field F = xi + yi through the cylindrical surface oriented away from the z-axis is zero.

In this case, the cylindrical surface is described by the equation 0 < z < 7. We can parameterize the surface using cylindrical coordinates as:

r(θ, z) = (r cos(θ), r sin(θ), z)

where r is the radius of the circular cross-section of the cylinder, and θ is the angle around the z-axis.

To compute the flux, we need to calculate the vector differential area element, dS. For a cylindrical surface, the vector differential area element can be written as:

dS = r dθ dz n

where r is the radius of the cylindrical surface, dθ is an infinitesimal angle element, dz is an infinitesimal height element, and n is the unit normal vector to the surface at each point.

Since the surface is oriented away from the z-axis, the unit normal vector is given by:

n = (cos(θ), sin(θ), 0)

Substituting the expression for dS and n into the surface integral formula, we have:

Flux = ∫∫S F · dS

= ∫∫S (xi + yi) · (r dθ dz n)

= ∫∫S (x cos(θ) + y sin(θ)) r dθ dz

Thus, the limits of integration for θ are 0 to 2π, and for z are 0 to 7.

Substituting the expression for F and the limits of integration into the surface integral, we have:

Flux = ∫ ∫0²π (rcos(θ) + rsin(θ)) r dθ dz

Evaluating the inner integral with respect to θ, we get:

Flux = ∫ [r²/2 sin(θ) - r²/2 cos(θ)] |0²π dz

Simplifying the expression, we have:

Flux = ∫ [0] dz

= 0

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9514 1404 393

Answer:

  72.18°

Step-by-step explanation:

The altitude of the front is 28 ft. It cuts the base in half, so the other leg of the right triangle is (18 ft)/2 = 9 ft. You know the tangent relation is ...

  Tan = Opposite/Adjacent

The angle of interest has opposite side 28 ft and adjacent side 9 ft, so we have ...

  tan(elevation angle) = (28 ft)/(9 ft)

  elevation angle = arctan(28/9)

  elevation angle ≈ 72.18°

The shape of the distribution  in histogram is skewed left and mean=43.071429 and standard deviation= 15.886445 are used together to measure the center and spread of the data.

What is histogram?

A grouped frequency distribution with continuous classes is graphically represented by a histogram. It is an area diagram, and its size is proportional to the frequencies in the associated classes. Due to the base's coverage of the spaces between class boundaries, all of the rectangles in such representations are contiguous.

We can make a sideways histogram. (makes it easier if typing text, but if you are writing on paper then you don't have to make it sideways) Each row will represent a range of 10 (1st row is 10 to 19, 2nd row is 20 to 29, etc)

=> 13 23 28 33 34 38 44 45 49 50 55 59 65 67

The data looks like it is slightly skewed left (hump towards the right [down]). The mean and the standard deviation are used together to measure the center and spread of the data.

Mean = \(\frac{ 13+23+28+33+34+38+44+45+49+50+55+59+65+67}{14}=\frac{603}{14}\) = 43.071429

Standard deviation = 15.886445

Hence the shape of the distribution  in histogram is skewed left and mean=43.071429 and standard deviation= 15.886445 are used together to measure the center and spread of the data.

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a continuous probability distribution the outcomes can take any value within a given range.

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Answer:

a = 155 degrees

Step-by-step explanation:

A straight line is equal to 180 degrees.

25 + a = 180

   Subtract 25 from both sides.

a = 155

I hope this was helpful to you! If it was, please consider rating, pressing thanks, and marking my answer Brainliest. It would help a lot. Have a great day!

Answer:

\(volume \: = 1130.4 {m}^{3} \)

Step-by-step explanation:

The formula to find the volume of a cylinder is:

\(v = \pi {r}^{2} h \\ basically \:it \:is\: the\: area \:of \:the \:circular \\ \:base\: \times\: \:height \:of \:the \:cylinder\)

Note that the radius is half the diameter (12), therefore the radius is 6*

According to the diagram we know that:

\(\pi = 3.14 \: \: \: r = 6 \: \: \: h = 10 \\ \\v = \pi {r}^{2} h\\ \\ v = (3.14)( {6}^{2} )(10) \\ \\ v = (3.14)(360) \\ \\ v = 1130.4 {m}^{3} \)

a) The Pearson correlation coefficient is 0.76.

b) Null hypothesis: There is no significant correlation between the grades in English and Mathematics (H0: r = 0)

Alternative hypothesis: There is a significant correlation between the grades in English and Mathematics (Ha: r ≠ 0)

c) The regression line is: y = 0.64x + 34.18

d) Interpretation and conclusion:  The Pearson correlation coefficient (r) of 0.76 indicates a strong positive correlation between the grades in English and Mathematics.

Correlation analysis:

Using the Pearson correlation coefficient to measure the strength and direction of the linear relationship between two variables.

Hypothesis testing:

Setting up null and alternative hypotheses, and using the t-test to determine whether the correlation coefficient is statistically significant.

Linear regression:

Finding the equation of the regression line that best describes the relationship between the two variables.

Interpretation and conclusion:

Using the results of the analysis to draw meaningful conclusions about the relationship between the two variables and the sample population as a whole.

Here we have

A study was conducted to determine the relationship existing between the grade in English and the grade in mathematics. a random sample of 10 students in uc was taken and the following are the results of the sampling

Student           1     2      3     4     5     6     7     8      9    10

English          75   83   80   77   89   78   92   86   93   84

Mathematics 78   87   78   76   92   81    89   89   91   84​  

a) To compute the Pearson correlation coefficient (r), first calculate the mean, standard deviation, and covariance of the two variables:

Mean of English grades (x)

= (75+83+80+77+89+78+92+86+93+84)/10 = 83.7

Mean of Math grades (y)

= (78+87+78+76+92+81+89+89+91+84)/10 = 84.5

The standard deviation of English grades (Sx)

= √((75-83.4)²+(83-83.4)²+...+(84-83.4)²)/9) = 6.52

The standard deviation of Math grades (Sy)

= √((78-84.4)²+(87-84.4)²+...+(84-84.4)²)/9) = 5.47

Covariance of the two variables

= ((75-83.4)(78-84.4)+(83-83.4)(87-84.4)+...+(84-83.4)(84-84.4))/9 = 26.6

Using the formula, r = cov(X,Y)/(SxSy),

we can calculate the correlation coefficient as follows

r = 26.6/(6.52*5.47) = 0.76

Therefore,

The Pearson correlation coefficient is 0.76.

b) Null hypothesis: There is no significant correlation between the grades in English and Mathematics (H0: r = 0)

Alternative hypothesis: There is a significant correlation between the grades in English and Mathematics (Ha: r ≠ 0)

c) To find the equation of the regression line, we need to calculate the slope (b) and the intercept (a) of the line. The formula for the slope is:

b = r(Sy/Sx) = 0.76(5.47/6.52) = 0.64

The formula for the intercept is:

=> a = y - bx = 84.4 - 0.64(83.4) = 34.18

Therefore,

The equation of the regression line is:

y = 0.64x + 34.18

Interpretation and conclusion:

The Pearson correlation coefficient (r) of 0.76 indicates a strong positive correlation between the grades in English and Mathematics.

The p-value associated with this correlation coefficient can be used to test the null hypothesis.

The equation of the regression line shows that for every one-point increase in the English grade, the predicted increase in the Mathematics grade is 0.64 points.

Therefore,

a) The Pearson correlation coefficient is 0.76.

b) Null hypothesis: There is no significant correlation between the grades in English and Mathematics (H0: r = 0)

Alternative hypothesis: There is a significant correlation between the grades in English and Mathematics (Ha: r ≠ 0)

c) The regression line is: y = 0.64x + 34.18

d) Interpretation and conclusion:  The Pearson correlation coefficient (r) of 0.76 indicates a strong positive correlation between the grades in English and Mathematics.

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Answer: yes

Step-by-step explanation:

12    3

4     1

to get to 3 from 12 you divide by 4 and to get from 4 to 1 you also divided by 4

Answer:

y-1=-3(x+2)

Step-by-step explanation:

Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

pls mark me as brainliest pls.

Answer:

-6.5y - 1.1x

Step-by-step explanation:

Rearrange the problem to where like terms are closer together:

11.7y+5.2y + 1.2x + x - 3.3x

Simplify by adding the like terms and your final answer will be -6.5y -1.1x

The yield to maturity of a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons, if the =bond is currently trading for a price of $884, is 6.23%. Thus, option a and option b is correct

Yield to maturity (YTM) is the anticipated overall return on a bond if it is held until maturity, considering all interest payments. To calculate YTM, you need to know the bond's price, coupon rate, face value, and the number of years until maturity.

The formula for calculating YTM is as follows:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

Where:

C = Interest payment

F = Face value

P = Market price

n = Number of coupon payments

Given that the bond has a coupon rate of 5.2%, a face value of $1000, a maturity of ten years, semi-annual coupon payments, and is currently trading at a price of $884, we can calculate the yield to maturity.

First, let's calculate the semi-annual coupon payment:

Semi-annual coupon rate = 5.2% / 2 = 2.6%

Face value = $1000

Market price = $884

Number of years remaining until maturity = 10 years

Number of semi-annual coupon payments = 2 x 10 = 20

Semi-annual coupon payment = Semi-annual coupon rate x Face value

Semi-annual coupon payment = 2.6% x $1000 = $26

Now, we can calculate the yield to maturity using the formula:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

YTM = (2 x $26 + ($1000-$884)/20) / (($1000+$884)/2) x 100

YTM = 6.23%

Therefore, If a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons is now selling at $884, the yield to maturity is 6.23%.

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Answer:

Step-by-step explanation:

Answer:

20/6

Step-by-step explanation:

16/6 is 2 4/6

6/6 is 1

3 is well 3

and 20/6 is 3 1/2