Fill in the missing number. % of 98 = 49

Answer: false

Step-by-step explanation:

Vertex of parabola = (-8 , -6)

Focus of parabola = (-8 , -23/4)

Directrix of parabola is y = -25/4

Axis of symmetry of parabola is x = -8

Direction of opening of parabola is vertically upwards.

y - intercept = 58 unit

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.

Given equation of parabola

y = x² + 16x + 58

It can be written as

y = x² + 16x + 64 - 6

y = (x + 8)² - 6

Comparing with standard vertex form

y = a(x - h)² + k

Vertex (h, k) = (-8 , -6), a = 1

a = 1/4(f - k)

1 = 1/4(f - -6)

4f + 24 = 1

f = -23/4

Focus (h , f) = (-8 , -23/4)

Directrix is y = d

Distance from the focus to the vertex is the same as the distance from the vertex to the directrix.

-6 - (-23/4) = d - (-6)

d = -6 -6 + 23/4

d = -12 + 23/4

d = -25/4

Directrix is y = -25/4

The axis of symmetry is the line perpendicular to the directrix that passes through the vertex and the focus:

x = -8

Direction of opening will be vertically upwards

For y-intercept, x = 0

y = (0 + 8)² - 6

y = 64 - 6

y = 58

Hence, (-8 , -6) is Vertex of parabola

(-8 , -23/4) is Focus of parabola

y = -25/4 is Directrix of parabola

x = -8 is Axis of symmetry of parabola

Direction of opening of parabola is vertically upwards.

58 unit is y - intercept

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7 test scores are 85 or greater according to the given scenario.

The third quartile (Q3) is a measure of central tendency that represents the value separating the lower 75% of a dataset from the upper 25%. In this case, the third quartile has a value of 85, meaning that 75% of the test scores are 85 or lower.

Since there are 30 exams in total, 30 x 0.75 = 22.5 exams have scores of 85 or lower. To find the number of exams with scores of 85 or greater, we subtract the number of exams with scores of 85 or lower from the total number of exams, which is 30 - 22.5 = 7. This means that 7 exams have scores of 85 or greater.

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Answer:

C = 200 + 50p

Step-by-step explanation:

Here's a table of values:

Number of phones (p) 0 1 2

Cost of materials and labor ($50p) 0 50 100

Total cost ($200 + $50p) 200 250 300

From the table, we can see that the total cost, C, is equal to the fixed cost of $200 plus the cost of materials and labor, which is $50 per phone produced. So, the equation representing the total cost in dollars of producing p phones in a given day is:

C = 200 + 50p

The size of a sample is related to the spread of the sampling distribution in that the larger the sample size, the less the spread.

As the sample size increases, the sampling distribution of p becomes increasingly concentrated around the true population proportion p. This is because, as the sample size increases, the number of possible random samples of size n becomes larger, making it more likely that the observed sample proportion will be close to the true population proportion.

The mean of the sampling distribution of p is p, which is the true population proportion. The standard deviation of the sampling distribution of p (σp) can be calculated using the formula:

σp = √((p)(1-p))/n

where p is the true population proportion and n is the sample size. This standard deviation indicates how closely the sample proportion is likely to match the true population proportion. The smaller the standard deviation, the more closely the observed sample proportion is likely to match the true population proportion.

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The path the bee needs to follow is A, E, L, M, N for it to arrive to its destination or flower.

To find the correct path, let's start in the first hexagon and let's move according to the answers. Here is the process:

Hexagon A: [tex]2^{4}[/tex]  

Hexagon E: 5 (4/4) = 5 x 1 = 5

Hegaxon L:  [tex]5^{3}[/tex] = 5 x 5 x 5 = 125

Hexagon M: 10 - [tex]2^{3}[/tex] + 3 = 10 - 8 + 3 = 2 + 3 =5

Hexagon N: (20-15) [tex]3^{3}[/tex] + 4 = 5 x 27 + 4 =135+4= 139

You have arrived to the hexagen S that is the flower

Based on this, the path to follow is A, E, L, M, and finally N from the strat to the flower.

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The equivalent expressions are  80x + 28y + 56 and -4(-20 + 7y - 14). Option C and D

Algebraic expressions are simply defined as expressions that are composed of variables, terms, constants, coefficients and factors.

They are also comprised of mathematical operations, such as;

From the information given, we have that;

8(-10x+3.5y-7)

Expand the bracket

80x - 28y + 56

Hence, the expressions are 80x + 28y + 56 and -4(-20 + 7y - 14)

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The complete question:

Which expressions are equivalent to 8(-10x+3.5y-7)? Select two options.

The vector orthogonal to the plane through the points P, Q, and R is (8, -8, 12), and the area of triangle PQR is [tex]$\sqrt{301}$[/tex].

For part (a), we can find a nonzero vector orthogonal to the plane through the points P, Q, and R by constructing a normal vector to the plane using the cross product of two vectors in the plane. The two vectors in the plane are [tex]$\vec{PQ} = (1- (-2), 0-1, 1-3) = (3, -1, -2)$[/tex] and [tex]$\vec{PR} = (1-4, 0-2, 1-5) = (-3, -2, -4)$[/tex]. Taking the cross product of the two vectors gives us the normal vector to the plane, [tex]$\vec{n} = \vec{PQ} \times \vec{PR} = (8, -8, 12)$[/tex]. Therefore, the vector orthogonal to the plane is [tex]$\vec{n} = (8, -8, 12)$.[/tex]

For part (b), the area of triangle PQR can be found using the formula for Heron's Formula, which states that the area of a triangle with sides a, b,and c is given by

[tex]$A = \sqrt{s(s-a)(s-b)(s-c)}$[/tex]

where [tex]$s = \frac{a+b+c}{2}$[/tex] . In this case, the sides are [tex]$a = \|\vec{PQ}\| = \sqrt{3^2 + (-1)^2 + (-2)^2} = \sqrt{14}$, $b = \|\vec{QR}\| = \sqrt{(-2-4)^2 + (1-2)^2 + (3-5)^2} = \sqrt{14}$[/tex], and[tex]$c = \|\vec{PR}\| = \sqrt{(-3)^2 + (-2)^2 + (-4)^2} = \sqrt{29}$[/tex]. Plugging these values into the formula, we get

[tex]= \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{\frac{7(7-\sqrt{14})(7-\sqrt{14})(7-\sqrt{29})}{4}} = \sqrt{7(7-\sqrt{14})^2(7-\sqrt{29})} = \sqrt{7(7-\sqrt{14})^2(\sqrt{14}+\sqrt{29})} = \sqrt{7(7-\sqrt{14})^2\sqrt{43}} = \sqrt{301}$[/tex]Therefore, the area of triangle PQR is [tex]$\sqrt{301}$[/tex]

The vector orthogonal to the plane through the points P, Q, and R is (8, -8, 12), and the area of triangle PQR is [tex]$\sqrt{301}$[/tex].

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Answer:

Marco had 45 dollars on the card when he received it.

Step-by-step explanation:

The correct answer is option (D). The answer is 100 on weekdays, 80 on weekends

Given that,

Ms. Liu wants to concentrate on growing her clientele and is looking for recurring business. She is less intrigued by visitors who are new to the site. The percentage of first-time users is 20%, according to analytics.

To find : What percentage of clients return on weekdays and weekends?

Number of repeat customer on weekdays = 125 * (1 - 20%) = 100

Number of repeat customer on weekend = 100 * (1 - 20%) = 80

Therefore, option is the appropriate response (D).The answer is 80 on weekends and 100 throughout the week.

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One other pair of coordinates that could be the missing ordered pair is (4, 0).

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Based on the information provided, we can logically deduce the following data points on the line:

At point (-2, -3), a linear equation of this line can be calculated in slope-intercept form as follows:

y + 3 = (-2 + 3)/(0 + 2)(x + 2)

y = 1/2(x + 2) - 3

y = 1/2x - 2

In this exercise, we would use an online graphing calculator to plot the linear function in order to determine the missing ordered pair (4, 0).

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Answer:

your total is $48

Step-by-step explanation:

8*6 (you plus five friends so six tickets and 8 dollars per ticket)

8 times 6 is 48

Pua will use 13, 1/4 cups of oatmeal.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Pua needs 3[tex]\frac{1}{4}[/tex] cups of oatmeal.

The number of 1/4 cups of oatmeal,

she will use,

= 13/4 ÷ 1/4

= 13

Therefore, she will use 13 cups.

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Answer:

Step-by-step explanation:19

You can't solve this question without further information of length and slope

Answer:

y=4x-7

Step-by-step explanation:

i hope it helped

Answer:5/5x-15/x

Step-by-step explanation:

Answer: your answer should be 3x^2 + 10x -75 / 5x.

Step-by-step explanation:

1. Combine multiplied terms into a single fraction

2. Find common denominator

3. Combine fractions with common denominator

4.  Multiply the numbers

5. Re-order terms so constants are on the left

6. Combine exponents

7. Multiply the numbers

8. Rearrange terms

therefore hopefully giving you the answer of 3x^2 + 10x -75 / 5x.

The required statements and reasons to prove that DE is equal to CE is explained.

The triangle congruence theorem is a theorem that can be used to prove that two or more triangles are the same, considering the corresponding properties of the triangles. The properties are length of the sides, and measure of internal angles.

The statements and reasons to prove that DE is equal to CE are explained below using the triangle congruence theorem.

         STATEMENT                            REASON

1. AD = BC                                          Given

2. <BCD = <ADC                                Given

3. DC = DC                                         Reflexive property

4. ΔADC ≅ ΔBCD                              SAS

5. <EDC ≅ <ECD                                CPCTC

6. AC = BD                                          Definition of diagonal

7. DE = CE                                           Congruent sides of isosceles triangle

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Jack will have $332 after 5 years

The formula for compound interest is:

A = P (1 + r/n)^(nt)

where:

A = the future value of the investment, including interest

P = the principal investment amount

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per year

t = the number of years the money is invested/borrowed for

r = 2% = 0.02, P =  $300, n = 12 (12 times in a year), t = 5 years

A = P (1 + r/n)^(nt)

A = 300 (1 + 0.02/12)^(12*5)

A = 300 (1 + 0.02/12)^(60)

A = $332

Thus, Jack will have $331.52 after 5 years

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The solution is Option C.

The system of equations have no solutions as they are parallel lines

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of first line be A

Let the equation of second line be B

Let the first point be P ( 0 , 3 )

Let the second point be Q ( 3 , 4 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 4 - 3 ) / ( 3 - 0 )

Slope m = 1/3

Now , the equation of line A is

y - y₁ = m ( x - x₁ )

y - 3 = ( 1/3 ) ( x - 0 )

y - 3 = ( 1/3 )x

Adding 3 on both sides of the equation , we get

y = ( 1/3 )x + 3   be equation (1)

And , the third point is R ( 0 , -2 )

Let the fourth point be S ( 3 , -1 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( -1 - ( -2 ) ) / ( 3 - 0 )

Slope m = 1/3

Now , the equation of line A is

y - y₁ = m ( x - x₁ )

y - ( -2 ) = ( 1/3 ) ( x - 0 )

y + 2 = ( 1/3 )x

Subtracting 2 on both sides of the equation , we get

y = ( 1/3 )x - 2   be equation (1)

Hence , the equations have the same slope as m = 1/3 and they are parallel lines

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Answer: 12%

12% is the right answer trust me

The surface area and volume of a sphere can be calculated using the following formulas:

Surface area: 4 * π * r^2

Volume: (4/3) * π * r^3

Where r is the radius of the sphere.

For the spheres given, the surface areas and volumes are:

(i) radius = 7 cm

Surface area: 4 * π * 7^2 = 4 * π * 49 = 196π cm^2

Volume: (4/3) * π * 7^3 = (4/3) * π * 343 = 588π cm^3

(ii) radius = 6.3 cm

Surface area: 4 * π * 6.3^2 = 4 * π * 39.69 = 158.48π cm^2

Volume: (4/3) * π * 6.3^3 = (4/3) * π * 251.187 = 447.938π cm^3

(iii) radius = 42 cm

Surface area: 4 * π * 42^2 = 4 * π * 1764 = 7056π cm^2

Volume: (4/3) * π * 42^3 = (4/3) * π * 74088 = 42672π cm^3

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Answer:

B

Step-by-step explanation:

Answer:

A. 37/100

Step-by-step explanation:

1. common denominator. so make 3/10 into 30/100.

2. subtract 30/100 from 67/100.

the answer is 37/100

As a result, the new length and breadth are 20% greater than the original specifications.

Percentages are just fractions with a denominator of 100. We use the percent sign (%) beside a number to indicate that it is a percentage. To calculate the percentage, divide the amount by the total value and multiply the result by 100. While many % numbers are between 0 and 100, there is no mathematical constraint that prevents percentages from taking on other values. Percentages are extensively utilized in a variety of contexts. Discounts in stores, bank interest rates, inflation rates, and numerous data in the media, for example, are all expressed as percentages. Percentages are essential for comprehending the financial elements of daily living.

Here,

If the original length and width of the living room floor are L and W, respectively, the new dimensions after increasing by 20% would be:

New Length = L + (0.20 * L) = L * 1.20

New Width = W + (0.20 * W) = W * 1.20

So the new length and width would be 20% larger than the original dimensions.

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There is a 0.3814 percent chance that a standard normal random variable will fall between 0.3 and 3.2.

In the posed query,

We must determine the likelihood that a standard normal random variable will occur with a probability between 0.3 and 3.2.

First, a standard normal random variable with a mean and standard deviation is introduced.

We must determine the likelihood that a standard normal random variable will fall within the range of 0.3 and 3.2.

The likelihood therefore should be

P(0.3<z<3.2)=P(z<3.2)−P(z<0.3)

Using z's typical value

P(0.3<z<3.2)=0.9993−0.6179

Simplifying

P(0.3<z<3.2)=0.3814

According to the z table, there is a 0.3814 percent chance that a standard normal random variable will fall between 0.3 and 3.2.

Option A is the proper response, so.

The complete question is:-

What is the probability that a standard normal random variable will be between .3 and 3.2?

A. .3814

B. .3808

C. .9993

D. .6179

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The number of vehicles Luann had in mind is 135.

The calculation of the number of vehicles Luann had in mind is based on the ratio of the number of predicted SUVs to the number of predicted vehicles, and the actual number of SUVs seen by Luann.

First, we know that for every 45 vehicles that pass by, 14 are expected to be SUVs. This means that 14/45 of the vehicles are expected to be SUVs.

Next, we know that Luann saw 42 SUVs pass by. To find the actual number of vehicles that have passed by, we set up a proportion:

We can then solve for the actual number of vehicles by cross-multiplying and dividing:

So the number of vehicles Luann had in mind is 135.

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Complete Question:

Luann predicted that if a certain number of vehicles passed by her by, 42 of them would be SUVs. What was the certain number of vehicles she had in mind?

Types of Vehicles  |   Number of vehicles

    Car                   |   6

  Truck                 |   10

    SUv                 |     14

 Minivan             |     15

The height of the statue of Abraham Lincoln memorial in Washington, DC, being 5.7912m is written as a single digit times an integer power of 10 as: 6 × 10^{-3} (approx)

The number is written in the form a*b^10 ,where we have 1<a<10

The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).

here, we have,

Scientific notations have some of the profits as:

Better readability due to compact representation

Its value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.

We're given that:

The height of the statue of Abraham Lincoln memorial in Washington, DC  is 5.7912 m.

We can rewrite it as:

5.7912 ≈ 6

Since we need to write it as a single digit times an integer power of 10, therefore, we get:

6 × 10^{-3} (approx)

Hence,The height of the statue of Abraham Lincoln memorial in Washington, DC, being 5.7912m is written as a single digit times an integer power of 10 as: 6 × 10^{-3} (approx)

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He is interested in studying the center, shape and spread of the data. He make histogram graph because it is the best since it demonstrates how the population is distributed.

A histogram is a graph that displays the frequency distribution of a small number of data points for a single variable. Frequently, histograms divide data into several "bins" or "range groups" and tally how many data points are in each bin.

A bar graph uses bars, columns, or strips to display facts, amounts, or numbers in a visual way.

To demonstrate how so much one factor influences others, scatter plots are used to display data points on the a vertical and horizontal axis.

A pie chart, also known as a circle chart, can be used to summarize a set of nominal data or to show the various values of a particular variable.

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The complete question is:

Someone is interested in studying property tax rates in the United States. He randomly selects 25 homes and looks up their property tax rate. He is interested in studying the center, shape and spread of the data. What type of graph does he make?

A. Histogram

B. Bar graphs

C. Scatterplots

D. Pie charts

The exponential equation in the standard form will be written as y = 250 (1.06)ˣ.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

When he first received it, he looked online and found that the value of the book was listed at $250. He checked again one year later and saw that the value has increased to $265.

Then the equations are given as,

250 = ab⁰

a = 250

265 = ab¹

265 = 250 b

b = 1.06

Then the exponential equation in the standard form will be written as,

y = 250 (1.06)ˣ

The exponential equation in the standard form will be written as y = 250 (1.06)ˣ.

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Answer:

Step-by-step explanation:

m

The answer choice that best describes the function x+ - 3 is D. The degree of the function is even, so the ends of the graph continue in opposite directions. Because the leading coefficient iS positive, the left side of the graph continues down the coordinate plane and the right side continues upward.

The graph of a function f in mathematics is the collection of ordered pairs where f(x)=y.

These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.

Given the function x+ - 3, the degre is even when plotted on a graph anf the left side of the graph continues down the coordinate plane and the right side continues upward.

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