What sentence represents the number of points in the problem below?
A test is worth 50 points. Multiple-choice questions are worth 1 point, and short-answer questions are worth 3 points. If the test has 20 questions, how many multiple-choice questions are there?
A. The number of multiple-choice question points plus the number of
short-answer question points is 20.
B. The number of multiple-choice question points minus the number
of short-answer question points is 20.
C. The number of multiple-choice question points times the number
of short-answer question points is 50.
D. The number of multiple-choice question points plus the number of
short-answer question points is 50.

The measure of angle RQT is 138⁰.

The measure of angle RQS is  48⁰.

The value of arc MN is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

The measure of angle RQT is calculated as follows;

m∠RQT = 180 - ( QR ) ( sum of angles on a straight line)

m∠RQT = 180 -  42⁰

m∠RQT = 138⁰

The measure of angle RQS is calculated as follows;

since line QS is the diameter of the circle, angle RQS must a right angle.

so angle SQT = 90 degrees.

m∠RQS = m∠RQT - m∠SQT

m∠RQS = 138 - 90

m∠RQS = 48⁰

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$45700\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &2 \end{cases}[/tex]

[tex]A = 45700\left(1+\frac{0.12}{4}\right)^{4\cdot 2}\implies A=45700(1.03)^8 \implies A \approx 57891.39 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{earned interest}}{57891.39~~ - ~~45700} ~~ \approx ~~ \text{\LARGE 12191.39}[/tex]

The smallest positive integer n such that t [tex]$\sqrt[4]{56 \cdot n}$[/tex]  is an integer is 686.

We have to find the smallest positive integer n such that [tex]$\sqrt[4]{56 \cdot n}$[/tex] is an integer

To find the smallest positive integer n such that  [tex]$\sqrt[4]{56 \cdot n}$[/tex]   is an integer, we need to determine the factors of 56 and find the smallest value of n that, when multiplied by 56, results in a perfect fourth power.

The prime factorization of 56 is:

56 = 2³ × 7

The prime factors of 56 need to be raised to multiples of 4.

Therefore, we need to determine the smallest value of n that includes additional factors of 2 and 7.

To make the expression a perfect fourth power, we need to raise 2 and 7 to the power of 4, which is 2⁴ × 7⁴

The smallest value of n that satisfies this condition is:

n = 2 × 7³ = 2× 343 = 686

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volume of the sphere is 113.1

Answer:

A. [tex]\frac{24}{25}[/tex]

The equation of the circle is (x + 4)² + (y - 6)² = 13.

To find the equation of the circle, we need the center coordinates and a point on the circumference. With the center at (-4, 6) and a point on the circumference at (-2, 9), we can determine the radius and write the equation of the circle in standard form.

First, let's calculate the radius using the distance formula. The distance between the center (-4, 6) and the point on the circumference (-2, 9) can be found as follows:

r = √[(x₂ - x₁)² + (y₂ - y₁)²]

r = √[(-2 - (-4))² + (9 - 6)²]

r = √[(2)² + (3)²]

r = √[4 + 9]

r = √13

So, the radius of the circle is √13.

Now we can write the equation of the circle in standard form:

(x - h)² + (y - k)² = r²

Using the center coordinates (-4, 6) and the radius √13, we have:

(x - (-4))² + (y - 6)² = (√13)²

(x + 4)² + (y - 6)² = 13

Therefore, the equation of the circle is (x + 4)² + (y - 6)² = 13.

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The area of the parallelogram is 42 cm².

The perimeter of the parallelogram is 48 cm.

Given a parallelogram ABCD.

We have to find the area and perimeter of the parallelogram.

Given,

AB = 14 cm and BC = 10 cm.

DE = 8 cm

Using Pythagoras theorem, height is,

CE = √(10² - 8²) = 6

Area of the parallelogram = 1/2 × 14 × 6

                                            = 42 cm²

Perimeter of the parallelogram = 2(14 + 10)

                                                    = 48 cm

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The number of coins in Ted and Mac's collection are 22 and 52 respectively

Ted's collection = x

Mac's collection = 8 + 2x

The expression which represents the number of coins in Mac's collection is 2x + 8

Ted's collection+Mac's collection= Total

x + (8 + 2x) = 74

3x + 8 = 74

3x = 74 - 8

3x = 66

x = 66/3

x = 22

Hence, Mac's collection would be 2(22)+8 = 52 while Ted's is 22

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The possible mixed number that could represent the amount he bought is 1/3  pounds of peanuts.

We are given that;

Amount layne bought= 2 and 3 peanuts

Now,

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

Thus,

To be able to determine how many peanuts and cashews Layne bought

2/3 pound of peanuts - 1/3 pound of cashews = 1/3 pounds

Therefore, by unitary method the answer will be 1/3 pounds.

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A. The range of class 2 is greater than the range of class 1. True.

B. The median of class 1 is greater than the range of class 2. False.

A. The range of a data set is the difference between the highest and lowest values in the set. In the dot plots, the highest value in class 2 is 10 and the lowest value is 6, so the range of class 2 is 10-6=4.

The highest value in class 1 is 9 and the lowest value is 1, so the range of class 1 is 9-1=8. Therefore, the range of class 2 is greater than the range of class 1.

B. The median of a data set is the middle value when the data is arranged in increasing order. In the dot plots, the median of class 1 is 5 and the median of class 2 is 7. Therefore, the median of class 1 is not greater than the range of class 2.

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Answer:

With the Pay-As-You-Go Calling Plan, licensed users can call out to numbers located in the country/region where their Microsoft 365 license is assigned to the user based on the user's location, and to international numbers in 196 countries/regions. Unlimited incoming minutes are included.

The probability of not rolling a 2 or a 5 on a 6-sided number cube is 2/3, or about 0.67 when expressed as a decimal.

The probability of rolling a 2 or a 5 on a 6-sided number cube is 2 out of 6 or 1/3, because there are two favorable outcomes (rolling a 2 or a 5) out of six possible outcomes.

The probability of not rolling a 2 or 5 is the complement of this probability.

In probability, the complement of an event is 1 minus the probability of that event.

So, to find the probability of not rolling a 2 or a 5, subtract the probability of rolling a 2 or 5 from 1.

That is, 1 - 1/3 = 2/3.

Therefore, the probability of not rolling a 2 or a 5 on a 6-sided number cube is 2/3, or about 0.67 when expressed as a decimal.

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The value of the angle U from the calculation is 88 degrees.

The sine rule can be applied in a variety of situations, such as determining a triangle's unknown side lengths or angles. The sine rule can be used to locate the missing side or angle if you know the lengths of two sides and the measure of an angle (not necessarily the included angle).

By the use of the sine rule;

u/Sin U = w/Sin W

Thus;

76/Sin U = 71/Sin 69

Sin U = 76Sin 69/71

U = Sin-1 (76Sin 69/71)

U = 88 degrees

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(√(2 + √2))/2 is the correct value of the cos(22.5)°.  Option (B) is correct using cos function.

To evaluate the exact value of cos(22.5 degrees) using the half-angle formula, we can make use of the half-angle identity for cosine:

cos(θ/2) = ±√((1 + cos(θ))/2)

Here, we have θ = 45 degrees, and we want to find cos(22.5 degrees).

Let's substitute the values into the cos function.:

cos(22.5 degrees) = ±√((1 + cos(45 degrees))/2)

Since we are dealing with a positive angle (22.5 degrees), we can take the positive square root in this case.

cos(22.5 degrees) = √((1 + cos(45 degrees))/2)

Now, we need to evaluate cos(45 degrees) to simplify the expression further. The value of cos(45 degrees) is √2/2.

cos(22.5 degrees) = √((1 + √2/2)/2)

Rationalizing the denominator:

cos(22.5 degrees) = √((2 + √2)/4)

Simplifying further:

cos(22.5 degrees) = √(2 + √2)/√4

cos(22.5 degrees) = √(2 + √2)/2

Therefore, the exact value of cos(22.5 degrees) using the half-angle formula is (√(2 + √2))/2.

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The solution to all the algebra expressions are:

28) 2³/₁₆

29) 6000

30) 132

28) The area of the rectangle formed by Shana's rug is given by the expression:

Area = Length * Width

Thus:

Area = 2⁵/₈ * ⁵/₆

= ²¹/₈ * ⁵/₆

= 35/16

= 2³/₁₆

29) We are given the number 2641.

Now, from right:

1 is in the units place

4 is in tens place

6 is in hundreds place

2 is in thousands place

If we switch 2 and 6, we will have:

6241 and as such 6 represents 6000

30) The expression is given as:

90 + 7 * (7 - 1)

Using PEMDAS order of operation gives us:

90 + 7(6)

= 90 + 42

= 132

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The last one, since obviously, there's no number that is at the same time greater than 3 and less than 2.

Answer:

24x

Step-by-step explanation:

Answer:

Step-by-step explanation:

There are an infinite amount of possibilities with the solution of (4,1).  As proof, plot the point (4,1) on a coordinate system.  Then, draw straight lines that pass through that point.  These lines can differ in slopes. They can be either be positive, negative, vertical, or horizontal.

x = 4

y = 1

x + y = 5

name me brainleist and say thank you, and rate 5 stars.

The solutions to the equation 2x² − 8x + 7 = 0 are x = 2.71 and x = -1.29.

The quadratic formula is:

x = (-b ± √(b² - 4ac)) / 2a

In this case, we have:

a = 2

b = -8

c = 7

Substituting these values into the quadratic formula, we get:

x = (-(-8) ± √((-8)² - 4(2)(7))) / 2(2)

x = (8 ± √(64 - 56)) / 4

x = (8 ± √8) / 4

x = (8 ± 2√2) / 4

x = 2 ± √2

x = 2.71 and x = -1.29

Therefore, the solutions to the equation 2x² − 8x + 7 = 0 are x = 2.71 and x = -1.29.

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The value of angle BAC is  43.5⁰.

The value of arc angle BC is  96⁰.

The value of angle 1 is 10⁰.

The value of angle BAC is calculated as follows;

m∠ BAC = ¹/₂ (BMC) (angle at center is half of the angle at circumference)

m∠ BAC = ¹/₂ ( 87 )

m∠ BAC = 43.5⁰

The value of arc angle BC is calculated by applying intersecting chord theorem as follows;

arc BC = 2 x m∠BAC (interior intersecting secants)

arc BC = 2 x 48⁰

arc BC = 96⁰

The value of angle 1 is calculated as follows;

m∠1 = ¹/₂ ( 85⁰ - (360 - (140 + 85 + 70) )

m∠1 = ¹/₂ (85 - 65 )

m∠1 = ¹/₂ (20)

m∠1 = 10⁰

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Answer:

1/2

Step-by-step explanation:

In a deck of cards, there are 13 hearts and 13 diamonds

13+13 = 26 hearts or diamonds

P( hearts or diamonds) = numbers of hearts or diamonds / total

                                       =26/52

                                       = 1/2

The coterminal angles of 5π/6 are 17π/6 and -7π/6.

We have,

A coterminal angle is an angle that ends at the same position as another angle on a standard coordinate plane.

Now,

To find coterminal angles, we can use the concept of adding or subtracting integer multiples of 2π (or 360 degrees) to the given angle. This is because adding or subtracting a full revolution (360 degrees or 2π radians) does not change the position of the angle on the coordinate plane.

In the case of the angle 5π/6, to find its coterminal angles, we can add or subtract multiples of 2π.

Adding 2π to the angle:

5π/6 + 2π = 5π/6 + 12π/6 = 17π/6

Subtracting 2π from the angle:

5π/6 - 2π = 5π/6 - 12π/6 = -7π/6

Therefore,

The coterminal angles of 5π/6 are 17π/6 and -7π/6.

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Based on the solution below, the number "8 ten thousands 16 thousands 12 hundreds and 17 ones" in standard form is 97,217.

For one to be able to write the given number in standard form, one need to add up the different place values and it will be:

8 ten thousands = 8 × 10,000

                           = 80,000

16 thousands = 16 × 1,000

                        = 16,000

12 hundreds = 12 × 100

                        = 1,200

17 ones = 17 × 1

                   = 17

After the above, one need to add them up and it will be:

80,000 + 16,000 + 1,200 + 17

= 97,217

Therefore, the number "8 ten thousands 16 thousands 12 hundreds and 17 ones" in standard form will be: 97,217.

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The total surface area of the figure is 144

From the question, we have the following parameters that can be used in our computation:

The net of the figure

The total surface area of the figure is the sum of the individual shapes

So, we have

Surface area = 9 * 9 + 7 * 9

Evaluate

Surface area = 144

Hence, the total surface area of the figure is 144

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[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ G(\stackrel{x_1}{5}~,~\stackrel{y_1}{-4})\qquad H(\stackrel{x_2}{11}~,~\stackrel{y_2}{0}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 11 +5}{2}~~~ ,~~~ \cfrac{ 0 -4}{2} \right) \implies \left(\cfrac{ 16 }{2}~~~ ,~~~ \cfrac{ -4 }{2} \right)\implies (8~~,~~-2)[/tex]

The expression 2¹⁰ - 1 is not a prime number. Because it has more than two factors.

Given that:

Expression, 2¹⁰ - 1

A prime number is a positive integer having exactly two factors which are 1 and the number itself. Any number that does not follow this is termed a composite number.

The value of the expression is given as,

⇒ 2¹⁰ - 1

⇒ 1,024 - 1

⇒ 1,023

The factor of 1,023 is given as,

1,023 = 3 x 11 x 31

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Answer:

$851, 786, 151, 000

Step-by-step explanation:

N =  A (1 + increase) ^n

Where N is future amount, A is initial amount, increase is percentage increase/decrease, n is number of mins/hours/days/months/years.

290 is our A value, increase is 8% (0.08), n is the number of years (2018 - 2004 = 14).

N =  290 (1 + 0.08) ^14

= 290 (1.08)^14

= $851, 786, 151, 000

Answer:

 (a) Parallelogram

  (c) Rhombus

Step-by-step explanation:

You want the names applicable to a quadrilateral with diagonals that bisect each other and bisect the vertex angles.

When the diagonals of a quadrilateral bisect each other, that quadrilateral is a parallelogram. With two pairs of parallel sides, the figure cannot be a trapezoid.

When both diagonals bisect the vertex angles, the quadrilateral is a rhombus.

The diagonals of a rectangle or square are congruent. The given figure labels the diagonals differently, so we cannot assume they are congruent. Hence the figure is not necessarily a rectangle or square.

The figure shown is a parallelogram that is a rhombus.

__

Additional comment

The figure doesn't have the crossing of diagonals marked as right angles, but they are. Segments 's' and 'x' are each altitudes of their respective isosceles triangles, so they must meet at right angles.

The relations shown in this figure can be used to prove a quadrilateral is a parallelogram and/or rhombus. That can be handy sometimes.

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The local maxima and minima of the given graph are at the points (-3, 0) and (0, 3)

We define a local minima/maxima as a point that is a minimum/maximum in a given region of the domain.

Here the local minimua and maxima are the two turning points that we can see on the graph.

Then the correct option is the last one, tha minima and maxima are (-3, 0) and (0, 3)

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The reference angle of -210 is 30 degrees and the sketch of the angle is attached

From the question, we have the following parameters that can be used in our computation:

Angle = 210 degrees

Rewrite as

θ = 210 degrees

The above angle is in the third quadrant

So, we subtract 180 degrees from it to calculate the reference angle

Using the above as a guide, we have the following:

Reference angle = 210 - 180

Evaluate the difference

Reference angle = 30 degrees

Hence, the reference angle is 30 degrees and the sketch of the angle is added as an attachment

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