Start of Questions
Write sinπ/5cosπ/8+cosπ/5sinπ/8 as a trigonometric function of one number. Keep π in your answer. Be sure to PREVIEW your answer before submitting!

Answer:

probability is 671 out of 1296 or 51.8 %.

Step-by-step explanation:

When we roll 4 fair 6-sided dice total outcomes are

 6^4 = 1296

The outcomes where no dice show greater than 5, the dice can show numbers 0,1,2,3,4,5

So the no of these outcomes where no dice show greater than 5 can be found by

5^4 = 625

No of outcomes where at least one dice will show number greater than 5 are

1296-625 = 671

Or in percentage,the probability is (671/1296)*100 = 51.8%

Answer:A randomization

Step-by-step explanation:Randomization in scientific experiments is a sampling method in which the participants or researchers are chosen randomly and assigned a treatment.

Here the participants or researchers do not know for sure which treatment is better.

Randomization reduces any possible bias responses to a minimal.

Since they are similar both dimensions would have the same ratio. The ratio of 5 and 15 is 3. 15 is 3 times larger than 5, so the unknown dimension is 3 times larger than the known dimension.

3 x 10 = 30

The unknown dimension is 30

Answer:

Step-by-step explanation:

Assuming the rate of increase in the cost of tuition fee per year is linear. We would apply the formula for determining the nth term of an arithmetic sequence which is expressed as

Tn = a + (n - 1)d

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = $20500(amount in 2000)

From 2000 to 2018, the number of terms is 19, hence,

n = 19

T19 = 454120

Therefore,

454120 = 20500 + (19 - 1)d

454120 - 20500 = 18d

18d = 433620

d = 433620/18

d = 24090

Therefore, the equation that can be used to find the tuition y for x years after 2000 is expressed as

y = 20500 + 24090(x - 1)

To to estimate the tuition at this college in 2020, the number of terms between 2000 and 2020 is 21, hence

x = 21

y = 20500 + 24090(21 - 1)

y = 20500 + 481800

y = $502300

Using linear interpolation, the yearly increase of tuition was calculated and an equation was formed. Substituting the year 2020 into the equation gave an estimated tuition of $47,855.60.

To write an equation that represents the tuition cost y for x years after 2000, we use two given data points: in 2000, tuition was $20,500 (which means when x=0, y=$20,500), and in 2018, tuition was $45,120 (when x=18, y=$45,120). To find the rate of change, we calculate the slope by finding the difference in tuition and dividing it by the difference in years:

Slope (m) = (Y2 - Y1) / (X2 - X1) = ($45,120 - $20,500) / (18 - 0) = $24,620 / 18 ≈ $1,367.78

Now we can write the equation of the line in slope-intercept form (y = mx + b), where b is the initial tuition in the year 2000:

Equation: y = 1367.78x + 20,500

To estimate the tuition in 2020, set x to 20:

y = 1367.78(20) + 20,500 = $27,355.60 + 20,500 = $47,855.60

Therefore, the estimated tuition in 2020 is $47,855.60.

Answer:

35

Step-by-step explanation:

Hi,

A simple way to look at this is making the pattern:

Red, Yellow

Red, Yellow, Blue

Red, Yellow, Blue, Green

Red, Yellow, Blue, Green, Pink

Red, Yellow, Blue, Green, Pink, Orange

Red, Yellow, Blue, Green, Pink, Orange, Purple

Red, Yellow, Blue, Green, Pink, Orange, Purple, White

2 + 3 + 4 + 5 + 6 + 7 + 8 = 35

You can otherwise use the Carl Gauss's formula for calculating the sum of increasing consecutive number:

[tex]Sum = \frac{n}{2} \ (a + b)[/tex]

where: n is the total number of rows;

a is the starting number of values and b is the ending number.

Hence, in this case:

n = 7

a = 2

b = 8

[tex]Total\ number\ of\ candles\ = \frac{7}{2}\ (2+8)\\ =35[/tex]

Final answer:

By analyzing the color pattern, which adds one new color each step and concludes with white being the eighth color, there are 8 total candles on the cake.

Explanation:

To determine how many total candles are on the cake with a color pattern that grows and ends with a white candle, we must first recognize the sequence of colors added as the pattern progresses. The given pattern is red, yellow; red, yellow, blue; red, yellow, blue, green, and continues adding in the order of pink, orange, purple, and finally white.

By this sequence, we can see that the color white will be the last in a set of eight candles (red, yellow, blue, green, pink, orange, purple, white). Since we are looking for the point at which the last candle is white, this indicates that the full sequence has been completed one time entirely. Therefore, there are 8 total candles on the cake.

Answer:

  d.  about 50 times larger

Step-by-step explanation:

The given expressions for magnitude (M) can be solved for the intensity (I). Then the ratio of intensities is ...

  [tex]\dfrac{I_2}{I_1}=\dfrac{I_0\cdot 10^{M_2}}{I_0\cdot 10^{M_1}}=10^{M_2-M_1}=10^{4.2-2.5}\\\\=10^{1.7}\approx 50[/tex]

The larger earthquake had about 50 times the intensity of the smaller one.

Answer:

  7.5

Step-by-step explanation:

For function f(x), the average rate of change between x=a and x=b is given by ...

  average rate of change = (f(b) -f(a))/(b -a)

For your function, this will be ...

  average rate of change = ((2^5 +3) -(2^1 +3))/(5 -1) = (35 -5)/4

  average rate of change = 7.5

Answer:

Well this question was hard ngl, but what I have learned in the previous years in 8th grade, the Area ≈93.53ft²

Step-by-step explanation:

If Im wrong I apologize but I believe thats the answer. You have an amazing day, you mean alot too this world, Y.O.L.O

Answer: 53 radical 3 or 93.53

Answer: the length of the arc is 15.17π feet

Step-by-step explanation:

The formula for determining the length of an arc is expressed as

Length of arc = θ/360 × 2πr

Where

θ represents the central angle.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Radius, r = 13 feet

θ = 210 degrees

Therefore,

Length of arc = 210/360 × 2 × π × 13

Length of arc = 15.167π feet

rounding up to 2 decimal places, it becomes

15.17π feet

Answer:

Andre can answer 1.5 multiplication facts in each second.

Step-by-step explanation:

Given:

Number of multiplication facts completed = 135

Number of second took to complete multiplication facts = 90 seconds.

We need to find the Number of facts answered per second.

Solution;

Now we know that;

In 90 seconds = 135 multiplication facts.

So in 1 second = Number of fact answered in 1 second

By Using Unitary method we get;

Number of fact answered in 1 second = [tex]\frac{135}{90}=1.5[/tex]

Hence Andre can answer 1.5 multiplication facts in each second.

Answer:

C

Step-by-step explanation:

35miles = 10days

x = 1day

10x = 35*1

x = 35/10

x = 3.5miles per day

Answer:

[tex]k=250[/tex]

Step-by-step explanation:

If y varies inversely with x, then

[tex]y=\dfrac{k}{x},[/tex]

where k is the constant of variation or the constant of inverse proportionality.

Since [tex]x=2.5[/tex] when [tex]y=100,[/tex] you have that

[tex]100=\dfrac{k}{2.5}[/tex]

Evaluate k:

[tex]k=100\cdot 2.5\\ \\k=250[/tex]

and

[tex]y=\dfrac{250}{x}[/tex]

Answer: [tex]x=5[/tex]

Step-by-step explanation:

The area of a rectangle can be found with the following formula:

[tex]A=lw[/tex]

Where "l" is the length and "w" is the width.

In this case you can identify in the figure given in the exercise that:

[tex]l=4x-2\\\\w=3[/tex]

You know that the area of that rectangle is the following:

[tex]A=54[/tex]

Therefore, knowing those values, you can substitute them into the formula and then you must solve for "x" in order to find its value. You get that this is:

[tex]54=(4x-2)(3)\\\\54=12x-6\\\\54+6=12x\\\\\frac{60}{12}=x\\\\x=5[/tex]

Answer:

64.08

Step-by-step explanation:

To find the angle of elevation of the sun, we use the tangent function with the height of the flagpole and the length of the shadow. Calculating the arctangent of the ratio of the height to the shadow length and converting it to degrees gives us the angle of elevation.

The question asks about the angle of elevation of the sun when casting the shortest shadow of a flagpole. We can use trigonometric functions to find this angle using the height of the flagpole and the length of the shadow. The height of the flagpole is 282 ft and the length of the shadow is 137 ft.

To find the angle of elevation (θ), we use the tangent function, which is the ratio of the opposite side (height of the flagpole) to the adjacent side (length of the shadow). So, tangent(θ) = opposite/adjacent = 282 ft / 137 ft.

Now, we will calculate the angle using the inverse of the tangent function, also known as arctangent.

θ = arctan(282/137)

To find the angle in degrees, we use a calculator to compute arctan(282/137). After computing, we round the result to the nearest whole number to find the angle of elevation to the nearest degree.

The length of MG is 56 for the given similar triangles.

Step-by-step explanation:

Let us consider EML and EGF is two similar triangles.

From the triangle,

EG=5x+2.

EM=16.

EL=28.

EF=126.

According to similar triangle property,

triangle ratio= [tex]\frac{EM}{EG} =\frac{EL}{EF} =\frac{ML}{GF} .[/tex]

[tex]\frac{16}{5x+2}=\frac{28}{126}[/tex].

126(16)=28(5x+2).

2016=140x+56.

140x=1960.

x=14.

⇒EG=5(14)+2.

EG=70+2.

EG=72.

To find the length of MG,

EG=EM+MG.

MG=EG-EM.

=72-16.

MG=56.

The question, asking for the length of a segment within a triangle, belongs to the field of Mathematics and is most likely at a High School level. However, based on the given information, an exact answer cannot be provided.

Unfortunately, the provided information is not sufficient enough to find the length of MG. The relationship EGF ~ EML indicates that the triangles EGF and EML are similar, meaning their corresponding sides are proportional. To find the length of MG (a segment within triangle EML), we would typically use a known length from triangle EGF and the scale factor between the two triangles. However, without these additional specifics, we cannot provide an exact value for the length of MG.

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Part 1: The function that models the height of the basketball is [tex]\( h(t) = -16t^2 + 15t + 6.5 \).[/tex]

Part 2: The basketball hits the ground after approximately 0.97 seconds.

Part 3: The basketball reaches its maximum height at approximately 0.47 seconds.

Part 4: The maximum height of the basketball is approximately 11.39 feet.

Part 1: To model the height of the basketball, we use the given function [tex]\( h(t) = -16t^2 + v0t + h0 \)[/tex] with the initial velocity [tex]\( v0 = 15 \)[/tex] ft/sec and the initial height [tex]\( h0 = 6.5 \)[/tex] feet. Plugging in these values, we get the function:

[tex]\[ h(t) = -16t^2 + 15t + 6.5 \][/tex]

Part 2: To find the time it takes for the basketball to hit the ground, we set the height function equal to zero and solve for [tex]\( t \)[/tex]:

[tex]\[ -16t^2 + 15t + 6.5 = 0 \][/tex]

Using the quadratic formula [tex]\( t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \),[/tex]where [tex]\( a = -16 \), \( b = 15 \)[/tex], and [tex]\( c = 6.5 \)[/tex], we get two solutions. We discard the negative solution because time cannot be negative, and we round the positive solution to the nearest hundredth:

[tex]\[ t = \frac{-15 \pm \sqrt{15^2 - 4(-16)(6.5)}}{2(-16)} \] \[ t = \frac{-15 \pm \sqrt{225 + 416}}{-32} \] \[ t = \frac{-15 \pm \sqrt{641}}{-32} \] \[ t \approx \frac{-15 + 25.31}{-32} \] \[ t \approx 0.97 \text{ seconds} \][/tex]

Part 3: To find when the basketball reaches its maximum height, we need to find the vertex of the parabola. The time coordinate of the vertex of a parabola [tex]\( ax^2 + bx + c \)[/tex] is given by [tex]\( t = -\frac{b}{2a} \)[/tex]. For our function, [tex]\( a = -16 \)[/tex]and [tex]\( b = 15 \)[/tex], so:

[tex]\[ t = -\frac{15}{2(-16)} \] \[ t = \frac{15}{32} \] \[ t \approx 0.47 \text{ seconds} \][/tex]

Part 4: To find the maximum height, we substitute the time at which the maximum height is reached back into the height function:

[tex]\[ h(0.47) = -16(0.47)^2 + 15(0.47) + 6.5 \] \[ h(0.47) \approx -16(0.2209) + 7.05 + 6.5 \] \[ h(0.47) \approx -3.5344 + 7.05 + 6.5 \] \[ h(0.47) \approx 11.39 \text{ feet} \][/tex]

Therefore, the basketball reaches a maximum height of approximately 11.39 feet after approximately 0.47 seconds.

Answer:

B=80 A=40 EFD=60 BCF=120

Step-by-step explanation:

First off chill. Second off B=80  A=40 EFD=60  BCF=120.  It is quite simple. The congruency marks give the first angle away and you solve from there. If you need help I would do more research because this is important for later units. Also the triangles are congruent.

Answer

Angle A = 40 degrees

Angle B = 80 degrees

Measure BCF = 120 degrees

Measure EFD = 60 degrees

Step-by-step explanation:

Angle A:

Ok, so we know angle A is congruent to angle D because of the line. If you make an equation out of it, you get 2x+20 = 3x+10. If you solve this equation:

2x + 20 = 3x + 10

20 = x+10

10 = x

you will get x=10. Plug it into the equation, and Angle A = 40 degrees.

Angle B:

The two lines that are both on angle B and E mean that they are congruent. We know that angle E = 80 degrees, so angle B does too.

Measure BCF:

We know that Angle A = 40 degrees, and angle B = 80 degrees. The degree sum of all angles in a triangle is 180 degrees.

80 + 40 = 120

180 - 120 = 60

So measure BCA = 60 degrees.

That angle is on a straight line. Two angles on a straight line add up to 180 degrees.

180 - 60 = 120.

So, Measure BCF = 120 degrees.

Measure EFD:

We already found measure BCA while finding measure BCF, and that is just congruent to EFD.

So, measure EFD = 60 degrees

Answer:

x = 3

JK = 13

KL = 13

JL = 26

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

K is midpoint JL. Use midpoint definition.

JK = 2x + 7

KL = 4x + 1

JK = KL

2x + 7 = 4x + 1

Step 2: Solve for x

Step 3: Find

JK

KL

JL

The variable x is found to equal 3. Substituting x=3 into the expressions for JK and KL, both are found to equal 13. The entire line segment JL is then found to equal 26.

In this mathematics problem, we are given that K is the midpoint of JL. This implies that the segments JK and KL are of equal length, thus JK=KL.

So, we can set the two given expressions equal to each other: 2x+7=4x+1. Solving this equation for x, we get that x=3.

Substituting x=3 into the expressions for JK and KL: JK=2x+7=2(3)+7=13, and KL=4x+1=4(3)+1=13.

To find JL, we simply add JK and KL together, since JKL is a line segment with K being the midpoint. Hence, JL=JK+KL=13+13=26.

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Answer:

200

Step-by-step explanation:

50 doubles to 100 and then doubles again to 200.

Answer:

Less

Step-by-step explanation:

The closer e is to 0, the more the ellipse will resemble a circle

Answer:

8/9 of a cup

Step-by-step explanation:

8 cups of icecream to be divided among 9 people, so they can't have full cups.

Each person will get 8/9 of a cup

Answer: the plant is 6 1/4 inches above the​ ground.

Step-by-step explanation:

In her garden Pam plants the seed 5 and one fourth inches below the ground. Converting 5 and one fourth inches to improper fraction, it becomes 21/4 inches.

After one month the tomato plant has grown a total of 11 and one half inches. Converting 11 and one half inches to improper fraction, it becomes 23/2 inches.

The height of the the plant above the​ ground would be

23/2 - 21/4 = (46 - 21)/4 = 25/4

Converting to mixed fraction, it becomes

6 1/4 inches

Your Question is incomplete, here is the complete statement of the question with the box plots in the attached file.

Question statement:

The box plots show the target heart rates of men 20-40 years old and men 50-70 years old.

Which statement is best supported by the information in the box plots?

A)

The range of the data for men 20-40 years old is less than the range of the

data for men 50-70 years old.

B)

The median of the data for men 20-40 years old is less than the median of

the data for men 50-70 years old.

o

The minimum target heart rate for men 20-40 years old is less than the

minimum target heart rate for men 50-70 years old.

D)

The interquartile range of the data for men 20-40 years old is greater than

the interquartile range of the data for men 50-70 years old.

Answer:

D

Step-by-step explanation:

please find the box plots in the file attached below.

looking at the box plots we can say that the answers is D due to following reasons:

Option A is incorrect:

The range of the data for men 20-40 years old is not less than the range of data for men 50-70 years old because  for men 20-40 years old range is 80 and for men 50-70 years old range is 70.

Option B is incorrect:

The median of the data for men 20-40 years old is not less than the range of data for men 50-70 years old because  for men 20-40 years old median is 130 and for men 50-70 years old median is 110.

Option C is incorrect:

The minimum target heart rate for men 20-40 years old is not less than the minimum target heart rate for men 50-70 years old because  for men 20-40 years old the minimum target heart rate is 90 and for men 50-70 years old the minimum target heart rate is 75.

Option D is correct:

The interquartile range of the data for men 20-40 years old is greater than the interquartile range of data for men 50-70 years old because  for men 20-40 years old interquarile range is  [tex]Q_{3}-Q_{1}=152.5-107.5=45[/tex] and for men 50-70 years old interquartile range is [tex]Q_{3} -Q_{1} =130-90=40[/tex].

Answer:

The answer to your question is below

Step-by-step explanation:

a) Yes, Joy can conclude that ΔABC is similar to ΔEDC because

∠ACB ≅ ∠ECD    they are vertical angles and,

∠ABC ≅ ∠EDC    they are right angles

We conclude that ΔABC is similar to ΔEDC  because of the AA postulate.

b)       [tex]\frac{AB}{BC} = \frac{DE}{CD}[/tex]

Solve for AB

        AB = (BC)(DE) / (CD)

Substitution

        AB = 105 (90) / 85

Simplification

        AB = 105(1.06)

Result

        AB = 111.2 ft

Answer:

Fred used 8 roses to make the bouquet.

Step-by-step explanation:

Let 'x' roses be used to make a bouquet.

Given:

Cost of carnations = $5.25

Cost of 1 rose = $1.68

Total cost of the bouquet = $18.69

Cost of 1 rose = $1.68

Therefore, using unitary method, the cost of 'x' roses is given as:

Cost of 'x' roses = [tex]1.68x[/tex]

Now, as per question:

Cost of carnations + Cost of 'x' roses = Total cost of the bouquet

[tex]5.25+1.68x=18.69\\\\1.68x=18.69-5.25\\\\1.68x=13.44\\\\x=\frac{13.44}{1.68}\\\\x=8[/tex]

Therefore, Fred used 8 roses to make the bouquet.

Fred used 8 roses in the bouquet.

To solve the problem, we need to find out how many roses Fred used, given the total cost of the bouquet and the cost of the carnations and each rose.

Let's denote the number of roses as ( r ).

The cost of one rose is $1.68. Therefore, the cost of ( r ) roses is ( 1.68r ).

The cost of the carnations is given as $5.25.

The total cost of the bouquet is $18.69.

We can set up the equation to represent the total cost of the bouquet as the sum of the cost of the carnations and the cost of the roses:

[tex]\[ 5.25 + 1.68r = 18.69 \][/tex]

Now, we need to solve for [tex]\( r \):[/tex]

Subtract $5.25 from both sides of the equation to isolate the term with [tex]\( r \):[/tex]

[tex]\[ 1.68r = 18.69 - 5.25 \][/tex]

[tex]\[ 1.68r = 13.44 \][/tex]

Next, divide both sides by $1.68 to solve for r :

[tex]\[ r = \frac{13.44}{1.68} \][/tex]

[tex]\[ r = 8 \][/tex]

Answer:

x = 110°

Step-by-step explanation:

I think that CHORDS AC & BD are intersecting at centre of the circle. If it is so then,

Since, measure of central angle of a circle is equal to the measure of its corresponding arc or vice versa.

Answer:

The answer to your question is x = 2.5

Step-by-step explanation:

We know that lines r and s are parallel so angles 1 and 2 are corresponding angles. Corresponding angles measure the same.

                                      m∠1 = m∠2

Substitution

                                40 - 4x = 50 - 8x

Solve for x

                               8x - 4x = 50 - 40

                                       4x = 10

                                         x = 10/4

                                         x = 2.5

Answer: the second one

Step-by-step explanation:

The surface area of the cone is [tex]266.9cm^2[/tex]

Explanation:

The diameter of the cone is 10 cms

Thus, the radius of the cone is given by

[tex]r=\frac{d}{2} =\frac{10}{2} =5[/tex]

The slant height of the cone is 12 cms

The formula for surface area of the cone is given by

[tex]$S A=\pi r^{2}+\pi r l$[/tex]

Substituting the values, we get,

[tex]$S A=(3.14)(5)^{2}+(3.14)(5)(12)$[/tex]

[tex]$S A=(3.14)25+(3.14)(60)$[/tex]

[tex]SA=78.5+188.4[/tex]

[tex]SA=266.9cm^2[/tex]

Thus, The surface area of the cone is [tex]266.9cm^2[/tex]

The surface area of the cone is approximately 268 square centimeters.

To find the surface area of a cone, we need to know the slant height and the radius of the base. The slant height is given as 12 centimeters. Since the diameter is 10 centimeters, we can find the radius by dividing the diameter by 2, which is 5 centimeters. Now we can use the formula for the surface area of a cone:

A = πr(r + l), where A is the surface area, r is the radius, and l is the slant height.

Plugging in the values, we get: A = 3.14 * 5(5 + 12) = 3.14 * 5 * 17 = 268.1 square centimeters. Rounding to the nearest whole number, the surface area of the cone is approximately 268 square centimeters.

Answer:

1) The possible outcomes 2) Quantitative 3) The explanation to those outcome 4) Qualitative

Step-by-step explanation:

1) The response variable is a measurable variable, i.e. also called the dependent variable. In the study, they will represent the possible outcome.

E.g.

Suppose the study "Practicing enhances technique", the amount of hours will be the response variable.

2) Is the response variable qualitative or​ quantitative? Since it is measured, it's a quantitative.

In our example, our response variable would be hours, how many hours is necessary to display some enhancement?

3) What is the explanatory​ variable?

The explanatory ones, or also independent variables offer explanations to the results the response variables have shown.

In our example, the level of training (low, mid, hard) would be the explanatory one.

4) Is the explanatory variable qualitative or​ quantitative?

In our example, the explanatory response or independent one is qualitative since to classify the training as low, middle or harder is to classify them as categorical then it's qualitative.

Answer:

The concepts being studied

Step-by-step explanation:

What are variables? ap e x