question 1. Enter the ratio equivalent to sin(B)

question 2. Consider this a right triangle. enter the measure of angle CAB to the nearest hundredth degree.

question 3. Suppose angle A is an angle such that angle cosA < sinA. select ALL angle measures that are possible values for angle A. 25, 35, 45, 55, 66, 75.

Answer:

There was 5% increase in visitors from last year to this year.

Step-by-step explanation:

Given:

Number of Visitors at theme park last year = 2000000

Number of Visitors at theme park this year = 2100000

We need to find the percent increase in visitors from last year to this year.

First we will find Number of increase in visitors from last year to this year.

Number of increase in visitors is equal to Number of Visitors at theme park this year minus Number of Visitors at theme park last year.

Framing in equation form we get;

Number of increase in visitors = 2100000 - 2000000 = 100000

Now Percent of increase in visitors is can be calculated by dividing Number of increase in visitors with Number of Visitors at theme park last year and then multiplied with 100.

Framing in equation form we get;

Percent of increase in visitors = [tex]\frac{100000}{2000000}\times 100 = 5\%[/tex]

Hence There was 5% increase in visitors from last year to this year.

There was a 5% increase in visitors to the theme park from last year to this year, calculated using the formula for percent increase.

The question is asking for the percent increase in visitors from one year to the next at a popular theme park. To find this, we'll use the formula for percent increase: ((new value - old value) / old value) * 100%.

In this case, the 'old value' is the number of visitors last year, which is 2,000,000. The 'new value' is the number of visitors this year, which is 2,100,000. Substituting these numbers into our formula gives us: ((2,100,000 - 2,000,000) / 2,000,000) * 100%.

This simplifies to: (100,000 / 2,000,000) * 100%. Then, converting 100,000 / 2,000,000 to a decimal gives us 0.05. Multiplying 0.05 by 100% gives us a 5% increase in visitors from last year to this year.

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Answer:

Step-by-step explanation:

Let x represent the total number of stdents that has all grades in the school.

There are three grades in the school. One grade has 1/3 of the students, this means that number of students that belongs tho this grade is 1/3 × x = x/3

One grade has 1/4 of the students, this means that number of students that belongs to this grade is 1/4 × x = x/4

Total number of students in both grades would be x/3 +/x/4 = 7x/12

The number of students in the remaining grade would be

x - 7x/12 = 5x/12

fraction of students in the remaining grade would be

(5x/12)/x = 5/12

Answer:

2/4

Step-by-step explanation:

i dont want to think

Answer:

D) 2, 4, 8, 16, 32

Step-by-step explanation:

We have given four sets of sequence.

And we have to find out which sequence is not an arithmetic sequence.

For this the given sequences should satisfy the value of common difference(d) and Arithmetic Progression formula.

A.P. Formula,

[tex]T_n=a+(n-1)d[/tex]

Where [tex]T_n[/tex] = nth term of an A.P.

a = first term of an A.P.

n = number of terms.

d = common difference.

'd' is calculated by subtracting fist term from second term.

[tex]d = second\ term-first\ term[/tex]

A) 4, 7, 10, 13, 16

[tex]d = 7-4=3[/tex]

[tex]d = 10-7=3[/tex]

Here d=3 and 5th term is 16.

So we find out the 5th term by using the formula of A.P. To check whether the sequence is in A.P. or not.

[tex]T_5=4+(5-1)3=4+4\times\ 3=4+12=16[/tex]

Here the given sequence fulfills the condition of being in A.P.

Hence the given sequence is an arithmetic sequence.

B) 1, 2, 3, 4, 5

[tex]d =2-1=1[/tex]

[tex]d =3-2=1[/tex]

Here d=1 and 5th term is 5.

[tex]T_5=1+(5-1)1=1+4=5[/tex]

Here the given sequence fulfills the condition of being in A.P.

Hence the given sequence is an arithmetic sequence.

C) 15, 9, 3, -3, -9

[tex]d =9-15=-6[/tex]

[tex]d =3-9=-6[/tex]

Here d=-6 and 5th term is -9.

[tex]T_5=15+(5-1)-6=15+4\times -6=15+(-24)=-9[/tex]

Here the given sequence fulfills the condition of being in A.P.

Hence the given sequence is an arithmetic sequence.

D) 2, 4, 8, 16, 32

[tex]d_1=4-2=2[/tex]

[tex]d_2=8-4=4[/tex]

Here [tex]d_1=2\ But\ d_2=4[/tex]

The common difference between the terms is not same.

In case of [tex]d_1[/tex].

[tex]T_5=2+(5-1)2=2+4\times 2=2+8=10[/tex]

In case of [tex]d_2[/tex].

[tex]T_5=2+(5-1)4=2+4\times 4=2+16=18[/tex]

Here the given sequence does not fulfills the condition of being in A.P.

Hence the given sequence is not an arithmetic sequence.

Hence the correct option is D) 2, 4, 8, 16, 32.

Answer:x1 = 1, x2 = - 1, x3 = 3

Step-by-step explanation:

x1 + 2x2 - x3 = - 4 - - - - - - - - - -1

x1 + 2x2 + x3 = 2 - - - - - - - - - -2

- x1 - x2 + 2x3 = 6 - - - - - - - - - -3

Let us eliminate x1 and x2. Subtracting equation 2 from equation 1, it becomes

-2x3 = - 6

x3 = -6/-2

x3 = 3

Adding equation 2 to equation 3, it becomes

x2 + 3x3 = 8 - - - - - - - - - - - 4

Substituting x3 = 3 into equation 4, it becomes

x2 + 3 × 3 = 8

x2 + 9 = 8

x2 = 8 - 9 = -1

Substituting x2 = -1 and x3 = 3 into equation 2, it becomes

x1 + 2 × -1 + 3 = 2

x1 - 2 + 3 = 2

x1 + 1 = 2

x1 = 2 - 1 = 1

Let us check by substituting x1 = 1, x2 = -1 and x3 = 3 into equation 1. It becomes

1 + 2 × - 1 - 3 = - 4

1 - 2 - 3 = - 4

-1 - 3 = - 4

-4 = - 4

Answer:

Step-by-step explanation:

Triangle TML is similar to triangle TVU.  Side TV measures 36 and side TM meaures 9; side TV is 4 times longer than side TM.  Same with sides VU and ML.  VU is 4 times longer than ML.  That means that side TU is 4 times longer than side TL.  Side TL measures x - 4; side TU measures 24 + x - 4 which is x + 20.  That means that x + 20 = 4(x - 4) and x + 20 = 4x - 16 and

3x = 36 so

x = 12

Answer:

99% confidence interval is:

(0.00278 < P1 - P2< 0.15921)

Step-by-step explanation:

For calculating a confidence intervale for the difference between the proportions of workers in the two cities, we calculate the following:

[tex][(p_{1} - p_{2}) \pm z_{\alpha/2} \sqrt{\frac{p_{1}(1-p_{1})}{n_{1}} + \frac{p_{2}(1-p_{2})}{n_{2}} }[/tex]

             Where  [tex]p_{1}[/tex] : proportion sample of individuals who worked      

                                                     at more than one job in the city one

                           [tex]n_{1}[/tex]: Number of respondents in the city one

                           [tex]p_{1}[/tex] : proportion sample of individuals who worked      

                                                     at more than one job in the city two

                           [tex]n_{1}[/tex]: Number of respondents in the city two

Then

α = 0.01 and α/2 = 0.005

and [tex]z_{\alpha/2} = 2.575[/tex]

[tex]p_{1} = \frac{112}{384} = 0.2916[/tex]

[tex]p_{2} = \frac{91}{432} = 0.2106[/tex]

[tex]n_{1}= 384[/tex]  and [tex]n_{2}= 432[/tex]

The confidence interval is:

[tex][(0.2916 - 0.2106) \pm 2.575 \sqrt{\frac{0.2916(1-0.2916)}{384} + \frac{0.2106(1-0.2106)}{432} }[/tex]

(0.00278 < P1 - P2< 0.15921)

Answer:

The correct answer is 14 not 17 or 7

Step-by-step explanation:

Answer:

[tex]5\frac{1}{4}[/tex] liters per hour.

Step-by-step explanation:

Consider the question: Ben drinks tea at an incredible rate. He drinks [tex]3\frac{1}{2}[/tex] liters of tea every [tex]\frac{2}{3}[/tex] of an hour. Ben drinks tea at a constant rate. How many liters of tea does he drink in one hour?

To find the liters of tea drank by Ben in one hour, we will divide amount of tea drank by time taken as:

[tex]3\frac{1}{2}\text{Liters}\div \frac{2}{3}\text{ hour}[/tex]

Convert mixed fraction into improper fraction:

[tex]\frac{7}{2}\text{Liters}\div \frac{2}{3}\text{ hour}[/tex]

Convert division problem into multiplication problem by flipping the 2nd fraction:

[tex]\frac{7}{2}\text{ Liters}\times \frac{3}{2}\text{ hour}[/tex]

[tex]\frac{21}{4}\frac{\text{ Liters}}{\text{ hour}}[/tex]

[tex]5\frac{1}{4}\frac{\text{ Liters}}{\text{ hour}}[/tex]

Therefore, Ben drinks [tex]5\frac{1}{4}[/tex] liters per hour.

Answer:

He drinks 21/4, or 5 1/4, liters of tea in 1 hour

Step-by-step explanation:

The following question is missing: How much does he drink in one hour?

Given that he drinks 3 1/2 (= 7/2) liters of tea every 2/3 of an hour, and we want to know how much he drink in 1 hour, then the following proportion must be satisfied:

7/2 liters / x liters = 2/3 hour / 1 hour

x = (7/2)/(2/3) = 7/2 * 3/2

x = 21/4 = 5 1/4 liters

Answer:

Correct answer: 4, 9, 25, 100

Step-by-step explanation:

Surface area of cylinder A = 2r²π + 2rπ h = 2rπ (r+h)

r₁ = 2r and h₁ = 2h => A₁ = 2 (2r) π (2r+2h) = 2 2rπ 2(r+h) = 4 2rπ (r+h)

A₁ = 4 A

r₁ = 3r and h₁ = 3h => A₁ = 2 (3r) π (3r+3h) = 3 2rπ 3(r+h) = 9 2rπ (r+h)

A₁ = 9 A   and so on......

God is with you!!!

Answer:

n = 3

Step-by-step explanation:

Answer:

see the explanation

Step-by-step explanation:

we know that

As the leading coefficient of the quadratic equation gets larger the parabola gets steeper and "narrower"

we have

[tex]f(x)=4x^{2}[/tex]

[tex]g(x)=\frac{15}{4}x^{2}[/tex]

[tex]h(x)=\frac{4}{15}x^{2}[/tex]

Compare the leading coefficients

The leading coefficient of f(x) is 4

The leading coefficient of g(x) is 15/4=3.75

The leading coefficient of h(x) is 4/15=0.27

so

4> 3.75> 0.27

therefore

f(x) is steeper than g(x) and h(x)

g(x) is steeper than h(x)

Verify each statement

1) f(x) is steeper than h(x)

The statement is true

2) h(x) is steeper than g(x)

The statement is false

3) g(x) is steeper than f(x)

The statement is false

Answer:

[tex]2\sqrt{2}\ ft\ longer[/tex]

Step-by-step explanation:

Area Of A Cube

Suppose a cube with side length s, the area of one side is

[tex]A_s=s^2[/tex]

Since the cube has 6 sides, the total area is

[tex]A=6A_s=6s^2[/tex]

But if we have the area, we can solve the above formula for s to get

[tex]A=6s^2[/tex]

[tex]\displaystyle s=\sqrt{\frac{A}{6}}[/tex]

We have two different cubes with areas 1,200 square inches and  768 square inches. Let's compute their side lengths

[tex]\displaystyle s_1=\sqrt{\frac{1,200}{6}}=\sqrt{200}[/tex]

[tex]\displaystyle s_1=10\sqrt{2}\ ft[/tex]

[tex]\displaystyle s_2=\sqrt{\frac{768}{6}}=\sqrt{128}[/tex]

[tex]\displaystyle s_2=8\sqrt{2} ft[/tex]

The difference between them is

[tex]10\sqrt{2}\ ft-8\sqrt{2}\ ft=2\sqrt{2}\ ft\approx 2.83\ ft[/tex]

The side of the cube with area 1,200 square inches is [tex]2\sqrt{2}\ ft[/tex] longer then the side of the cube with area 768 square inches

Answer:

Its B

Step-by-step explanation:

Edge 2021

Answer:

100.75 liters

Step-by-step explanation:

Data provided in the question:

t (min)     0     0.5      1     1.5      2      2.5      3

r (l/min)    44    40     37     34     30     27      23

Now,

left endpoint approximation

= 0.5 × ( 44 + 40 + 37 + 34 + 30 + 27 )

= 0.5 × 212

= 106

Right endpoint approximation

= 0.5 × ( 40 + 37 + 34 + 30 + 27 + 23 )

= 0.5 × 191

= 95.5

Therefore,

the average of the left- and right-endpoint approximations

= [ 106 + 95.5 ] ÷ 2

= 100.75 liters

The total amount of water drained during the first 3 min is: 100.75 liters/min.

Left endpoint approximation

r = 1/2 ( 44 + 40 + 37 + 34 + 30 + 27 )

r= 1/2 × 212

r= 106 L/m

Right endpoint approximation

r= 1/2 × ( 40 + 37 + 34 + 30 + 27 + 23 )

r= 1/2 × 191

r= 95.5 L/min

Average of the left- and right-endpoint approximations

Average= [ 106 + 95.5 ] ÷ 2

Average=201.5÷2

Average= 100.75 liters/min

Inconclusion the total amount of water drained during the first 3 min is: 100.75 liters/min.

Learn more about total amount of water here:https://brainly.com/question/26007201

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]x+5y\geq 5[/tex] ----> inequality A

The solution of the inequality A is the shaded area above the solid line [tex]x+5y=5[/tex]

The slope of the solid line is negative

The y-intercept of the solid line is (0,1)

The x-intercept of the solid line is (5,0)

[tex]y\leq 2x+4[/tex] ----> inequality B

The solution of the inequality B is the shaded area below the solid line [tex]y= 2x+4[/tex]

The slope of the solid line is positive

The y-intercept of the solid line is (0,4)

The x-intercept of the solid line is (-2,0)

therefore

The graph in the attached figure

Answer:

30

Plz click the thxs button or mark brainliest!

Yours Truly.

Answer:

30

Step-by-step explanation:

2 2 10 6

3 1 5 3

5 1 5 1

1 1 1

2*3*5 30

You need to buy 400 square feet of dirt for both companies to charge the same

Solution:

Given that,

Company A sells dirt for $137.5 for 50 square feet and has a delivery fee of $100 dollars

Dirt sold for $137.5 for 50 square feet

Let us find dirt sold for 1 square feet:

50 square feet = $ 137.5

1 square feet = [tex]\frac{137.5}{50} = 2.75[/tex]

Thus dirt sold for $2.75 for 1 square feet

Company A has a delivery fee of $ 100 dollars

Amount Charged by company A:

Let "x" be the amount of dirt bought for 1 square feet

A = 2.75(x) + 100

A = 2.75x + 100 --- eqn 1

Company B sells dirt for $15 for 5 square feet and offers free delivery

Dirt sold for $ 15 for 5 square feet

5 square feet = $ 15

1 square feet = [tex]\frac{15}{5} = 3[/tex]

Thus dirt sold for $ 3 for 1 square feet

Company B offers free delivery

Amount Charged by company B:

A = 3x  ---- eqn 2

Let us equate eqn 1 and eqn 2 to find the dirt you need to buy for both companies to charge the same

2.75x + 100 = 3x

3x - 2.75x = 100

0.25x = 100

x = 400

Thus you need to buy 400 square feet of dirt for both companies to charge the same

Answer:

See proof below

Step-by-step explanation:

We denote (x,y)∈R as xRy, and we also use the similar notation xSy for (x,y)∈S. Remember that R and S are reflexive, antisymmetric and transitive relations (the definition of partial order).

To prove that R∩S⊆A is a partial order, we will prove that R∩S is reflexive, antisymmetric and transitive.

There is an error in the equation provided. Looking at other similar question such as this, I think the equation related to x and y should be 90x + 1600 = y

Answer:

a) 90

b) 1600

Step-by-step explanation:

The equation 90x + 1600 = y is an equation of a straight line in the form y = mc + c

Adjusting the equation to the general form we get

y = 90x + 1600

m = 90

c = 1600

a) the change in Mary's total pay for each copy she sells in this case is referring to the change of y to the change of x.

In other word, it is the slope of the function.

m = 90

b) if Mary didn't sell any copies, the value of x will be 0.

In graph of a straight line, the value when x= 0 is at the value of y-intercept,

c = 1600

Answer:

Speed of Faster jet is 756 miles/hr and speed of slower jet is 685 miles/hr.

Step-by-step explanation:

Let the speed of faster jet be represent as 's'

Now Given:

one jet travels 71 mih slower than the other.

Hence Speed of slower jet will be = [tex]s-71[/tex]

Distance = 5764 miles

Time = 4 hrs

Now we know that;

Distance is equal to product of speed and time.

Framing in equation for we get;

Distance = (Speed of Faster Jet + Speed of Slower jet) × Time.

Substituting the given values we get;

[tex]5764=(s+s-71)\times 4\\\\5764= (2s-71)\times 4\\\\\frac{5764}{4} = 2s-71\\\\1441=2s-71\\\\2s=1441+71\\\\2s =1512\\\\s =\frac{1512}{2} = 756\ mi/h[/tex]

Speed of faster jet = 756 miles/hr

Speed of slower jet = [tex]s-71 =756-71 = 685\ mi/hr[/tex]

Hence Speed of Faster jet is 756 miles/hr and speed of slower jet is 685 miles/hr.

Now we will check the answer;

Distance traveled by faster jet = speed × time = 756 × 4 = 3024 miles.

Distance traveled by Slower jet = speed × time = 685 × 4 = 2740 miles

Hence Total Distance = 3024 + 2740 = 5764 miles.

Answer:

Not mutually exclusive

Step-by-step explanation:

In the rule of probability, for two events to be mutually exclusive, the probability of them occuring at the same time must be 0.

In this case P(true and false) = 0 to be mutually exclusive.

In the term of Vann diagram 'true and false' in this case represent the intersection of two events 'true' and 'false'. And if it is shown in Vann diagram, both group will be apart from each other or the value inside the Vann diagram is 0.

Therefore,

We know from statistics that

P(A and B) = P(A) + P(B) - P(A or B)

Translating into this case

P(true or false) = P(true) + P(false) - P(true and false)

= 0.9 + 0.82 - 0.75 = 0.97

Therefore, this event is not mutually exclusive.

Answer:

no and 0.97

Step-by-step explanation:

Answer:

At Present Jane has Total Stickers = 251

Step-by-step explanation:

Stickers Initially = 27

Jane bought stickers on 1st day = 3

Remaining days = 13

Each next day she bought 2 more stickers than the previous day, so:

Stickers bought in the last 2 weeks (14 days) = n+(n+2)+(n+2+2)+(n+2+2+2)+.............+(n+2(13))

here n =3

So:

Stickers bought in the last 2 weeks (14 days) = 3+5+7+9+11+13+15+17+19+21+23+25+27+29

Stickers bought in the last 2 weeks (14 days) = 224

At Present Jane has Total Stickers = Stickers Initially+ Stickers bought in the last 2 weeks (14 days)

At Present Jane has Total Stickers = 27+224

At Present Jane has Total Stickers = 251

Answer:

30% companies will offer both wireless internet and free on-board snacks.

Step-by-step explanation:

Percentage of major companies who equip their planes with wireless internet access = 30%

Percentage of major airlines who offer passengers free on-board snacks = 70%

Therefore, from the given information, the maximum percentage of the companies who offer both wireless internet facility as well as on-board snacks may be 30% only.

Answer:

[tex]y=0.00673(253) +90.190=91.894[/tex]

And the difference is given by:

[tex]r_i =91.894-83=8.894[/tex]

Step-by-step explanation

We assume that th data is this one:

x: 242-255 -227-251-262-207-140

y: 91- 81 -91 - 92 - 102 - 94 - 91

Find the least-squares line appropriate for this data.  

For this case we need to calculate the slope with the following formula:

[tex]m=\frac{S_{xy}}{S_{xx}}[/tex]

Where:

[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}[/tex]

[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}[/tex]

So we can find the sums like this:

[tex]\sum_{i=1}^n x_i =242+255+227+251+262+207+140=1584[/tex]

[tex]\sum_{i=1}^n y_i =91+ 81 +91 + 92 + 102 + 94 + 91=642[/tex]

[tex]\sum_{i=1}^n x^2_i =242^2 +255 ^2 +227^2 +251^2 +262^2 +207^2 +140^2=369212[/tex]

[tex]\sum_{i=1}^n y^2_i =91^2 + 81 ^2 +91 ^2 + 92 ^2 + 102 ^2 + 94 ^2 + 91^2=59108[/tex]

[tex]\sum_{i=1}^n x_i y_i =242*91 +255*81 +227*91 +251*92 +262*102 +207*94 +140*91=145348[/tex]

With these we can find the sums:

[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=369212-\frac{1584^2}{7}=10775.429[/tex]

[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=145348-\frac{1584*642}{7}=72.571[/tex]

And the slope would be:

[tex]m=\frac{72.571}{10775.429}=0.00673[/tex]

Now we can find the means for x and y like this:

[tex]\bar x= \frac{\sum x_i}{n}=\frac{1584}{7}=226.286[/tex]

[tex]\bar y= \frac{\sum y_i}{n}=\frac{642}{7}=91.714[/tex]

And we can find the intercept using this:

[tex]b=\bar y -m \bar x=91.714-(0.00673*226.286)=90.190[/tex]

So the line would be given by:

[tex]y=0.00673 x +90.190[/tex]

The prediction for 253 seconds is:

[tex]y=0.00673(253) +90.190=91.894[/tex]

And the difference is given by:

[tex]r_i =91.894-83=8.894[/tex]

Answer:

100 miles

Step-by-step explanation:

Let

x ----> the number of miles driven

y ---> the total cost

we know that

The linear equation in slope intercept form is equal  to

[tex]y=mx+b[/tex]

where

m is the slope or unit rate of the linear equation

b is the y-intercept or initial value

In this problem we have

First Plan

The slope is equal to [tex]m=\$0.15\ per\ mile[/tex]

The y-intercept is [tex]b=\$54[/tex]

so

The linear equation is

[tex]y=0.15x+54[/tex] -----> equation A

Second Plan

The slope is equal to [tex]m=\$0.10\ per\ mile[/tex]

The y-intercept is [tex]b=\$59[/tex]

so

The linear equation is

[tex]y=0.10x+59[/tex] -----> equation B

To find out for what amount of driving do the two plans cost the same, equate equation A and equation B

[tex]0.15x+54=0.10x+59[/tex]

solve for x

[tex]0.15x-0.10x=59-54[/tex]

[tex]0.05x=5[/tex]

[tex]x=100\ miles[/tex]

Find the cost

for x=100 miles  

substitute in equation A or equation B (the cost is the same)

[tex]y=0.15(100)+54=\$69[/tex]

Final answer:

The two car rental plans cost the same for 100 miles driven. To find this, the total cost equations for both plans are set equal to each other, and the resulting equation is solved for the number of miles.

Explanation:

To determine when the two car rental plans cost the same, we need to set up and solve an equation where the total costs of both plans are equal. We will let x represent the number of miles driven.

Cost Equations for Two Plans:

Plan 1: $54 + $0.15x

Plan 2: $59 + $0.10x

To find where they cost the same, we set the cost equations equal to each other:

54 + 0.15x = 59 + 0.10x

We then solve for x by first subtracting $0.10x from both sides:

54 + 0.05x = 59

Next, we subtract $54 from both sides:

0.05x = 5

Finally, we divide both sides by 0.05:

x = 100

Therefore, the two plans cost the same when Martina drives 100 miles.

Answer:

The required sum of the digits in that integer is 440.

Step-by-step explanation:

Consider the provided expression.

[tex]10^{50}-74[/tex]

We need to find the sum of the digits in that integer.

For [tex]10^2[/tex] = 100 (3 digits)

Now subtract 74 from it.

100-74=26

For [tex]10^3[/tex] = 1000 (4 digits)

Now subtract 74 from it.

1000-74=926

For [tex]10^4[/tex] = 100000 (5 digits)

Now subtract 74 from it.

10000-74=9926

Similarly,

[tex]10^50[/tex] = 1000....[51 digits]

Now subtract 74 from it.

[tex]10^50-74=99999....26[/tex]

The number of 9 after subtracting 74 is 3 less than the number of digits.

Therefore, the number of 9 after subtracting 74 from [tex]10^50[/tex] must be: 51-3=48

The sum of the digits is = 9×48 + 2 + 6 = 432 + 2 + 6 = 440.

Hence, the required sum of the digits in that integer is 440.

Final answer:

The sum of the digits in the integer 10⁵⁴ - 74 is 476, which is calculated by adding the contribution of the 52 nines and the digits in '26'.

Explanation:

To determine the sum of the digits of the integer written in base decimal notation for 10⁵⁴ - 74, we first need to understand what 10⁵⁴ represents. This value is a 1 followed by 54 zeros in decimal form. When we subtract 74 from this value, we alter only the last two non-zero digits. This results in a number that looks like 999...9926, where the '9's continue until the last two digits, which are '26'.

To find the sum of the digits, we simply add up the '9's and '26'. Since there are 52 nines (54 digits minus the last two which are '26'), and each nine contributes nine to the sum, we can calculate this part of the sum as 52 multiplied by 9. Then we also add the sum of the digits in '26'.

Therefore, the sum of digits in 10⁵⁴ - 74 is (52 × 9) + 2 + 6 = 468 + 8 = 476.

1) Which angle is not coterminal to 120 degrees?

A. 840

B. -180

C. 480

From given options, -180 is not a coterminal angle of 120 degrees

Coterminal Angles are angles who share the same initial side and terminal sides.

Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians

Coterminal angles of 120 degrees are:

120 degrees + 360 degrees = 480 degrees

120 degrees - 360 degrees = 240 degrees

720 degrees + 120 degrees = 840 degrees

120 degrees - 720 degrees = -600 degrees

Therefore:

Positive Angle 1 (Degrees) 480

Positive Angle 2 (Degrees) 840

Negative Angle 1 (Degrees) -240

Negative Angle 2 (Degrees) -600

Therefore from given options, -180 is not a coterminal angle of 120 degrees

A. Cos theta = undefined

B. Sin theta = -1

C. Tan theta = 0

Sin theta = -1  is correct

given angle is -90

Find the reference angle for -90

Reference angle = 360 - 90 = 270 degrees

Unit circle diagram is attached below

And from the unit circle, we know the coordinates for  270 degrees are (0, -1)

Our angle - 90 degrees lies in (0, -1)

Unit circle coordinates are given by  [tex](cos \theta , sin \theta )[/tex]

This means,

cos (-90 ) = 0 and sin(-90) = -1

We know that,

[tex]tan \theta = \frac{sin \theta}{cos \theta}[/tex]

[tex]tan \theta = \frac{-1}{0}[/tex] = undefined

Therefore from options, sin theta = -1 is correct

Answer:

Step-by-step explanation:

It is the fourth one

Hope this helps

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Answer:

E. $6,154

Step-by-step explanation:

Let x represent selling price of the bond.

We have been given that last year a certain bond with a face value of $5,000 yielded 8 percent of its face value in interest.

Let us calculate 8% of $5,000 to find amount of interest as:

[tex]\text{Amount of interest }=\$5,000\times \frac{8}{100}[/tex]

[tex]\text{Amount of interest }=\$50\times 8[/tex]

[tex]\text{Amount of interest }=\$400[/tex]

We are also told that the amount of interest was approximately 6.5 percent of the bond's selling price. 6.5 percent of the bond's selling price would be [tex]\frac{6.5}{100}x[/tex].

We can represent our given information in an equation as:

[tex]\frac{6.5}{100}x=\$400[/tex]

[tex]100*\frac{6.5}{100}x=\$400*100[/tex]

[tex]6.5x=\$40,000[/tex]

[tex]\frac{6.5x}{6.5}=\frac{\$40,000}{6.5}[/tex]

[tex]x=\$6,153.846153846[/tex]

[tex]x\approx \$6,154[/tex]

Therefore, the selling price of the bond was approximately $6,154 and option E is the correct choice.

Answer: 10

Step-by-step explanation:

Since integral from 1 to 4 of f(x) =10

To evaluate integral from 2 to 8 of 2 times f(2x), using substitution method

Let U = 2x, dU = 2dx, dx = dU/2

Evaluate the limit, upper limit gives dU = 2*4 = 8, lower limit gives dU = 2*1 = 2.

Since this limit are the same as the limit for the question,

Therefore, F(4) - F(1) = F(8) - F(2) = 10

Substituting dx=dU/2

Gives,

Integral from 2 to 8 of 2 times f(2x)= (1/2)(2)(F(8)-F(2)) = 10

Answer

Step-by-step explanation:

answer c