Speedometer readings for a vehicle (in motion) at 15 -second intervals are given in the table below. Estimate the distance traveled by the vehicle during this 90 -second period using six rectangles and left endpoints. Repeat this calculation twice more, using right endpoints and then midpoints.
t(sec) 0 15 30 45 60 75 90
v(ft/s) 0 10 35 62 79 76 56

The 20th prize is $4400.

It is a sequence where the difference between each consecutive terms is the same.

Example:

2, 4, 6, 8 is an arithmetic sequence.

We have,

First prize = $12,000

Successive prize worth $400 less than the preceding prize.

Now,

We can make an arithmetic sequence.

12,000, 11,600, 11,200, ...

So,

a = 12,000

d = -400

The nth term of an arithmetic sequence.

= a + (n - 1)d

So,

The 20th prize.

= 12,000 + (20 -1)400

= 12,000 - 19 x 400

= 12,000 - 7600

= 4400

Thus,

20th prize = $4400

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Answer:

x₁ = (1 + √43)/6

x₂ = (1 - √43)/6

Step-by-step explanation:

6x² - 2x = 7

6x² - 2x - 7 = 0

Formula

ax² + bx + c = 0

a = 6 ; b = - 2 ; c = - 7

x₁/₂ = [-b ± √(b²- 4ac)]/2a

x₁/₂ = (2 ± √4 + 4×6×-7)/12

x₁/₂ = (2 ± √172)/12

x₁/₂ = (2 ± 2√43)/12

x₁/₂ = 2(1 ± √43)/12

x₁/₂ = (1 ± √43)/6

x₁ = (1 + √43)/6

x₂ = (1 - √43)/6

Answer:

238 D

Step-by-step explanation:

238 lol. 34 times 7 is 238

Answer:

D. There are 238 peanuts in each box.

Step-by-step explanation:

It is simple:

34x7=238

Please can I have brainliest I need 2 more brainliest to lvl up, so can I please, please, please have brainliest?!

Respuesta:

x = 5.656854249

Explicación paso a paso:

[NOTA: Solo quería disculparme de antemano por cualquier mala gramática, ya que estoy usando un traductor para esto.]

x/Sen30°= 8/Sen45° [Multiplica ambos lados por Sen30°]

x = (8/Sen45°) * Sen30° [Resuelve usando una calculadora]

x = 5.656854249

The probability is a very small value, and when expressed as a decimal rounded to the nearest millionth, it is approximately 0.000011

The probability that the four flavors chosen consist of each of their favorite flavors can be calculated by considering the total number of possible outcomes and the number of favorable outcomes.

First, let's determine the total number of possible outcomes. Since there are 40 flavors in total and they are randomly choosing four flavors, the total number of possible outcomes can be calculated using combinations. We can use the formula for combinations: nCr = n! / (r!(n-r)!), where n is the total number of flavors (40) and r is the number of flavors they are choosing (4).

nCr = 40! / (4!(40-4)!)

    = 40! / (4!36!)

    = (40 * 39 * 38 * 37) / (4 * 3 * 2 * 1)

    = 91390

Next, let's determine the number of favorable outcomes, which is the number of ways they can choose one flavor from each of their favorites. Since each person has a different favorite flavor, the number of favorable outcomes is simply 1 for each person.

Therefore, the probability of choosing four flavors consisting of each of their favorite flavors is:

Probability = Number of favorable outcomes / Total number of possible outcomes

           = (1 * 1 * 1 * 1) / 91390

           = 1 / 91390

The probability is a very small value, and when expressed as a decimal rounded to the nearest millionth, it is approximately 0.000011.

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Answer:

16.32.5

17.1.32

18.3.25

19.540

20.5.49

21.4.75

Step-by-step explanation:

Answer:

16=$32.5

17=$1.32

18=$3.25

19=$540

20=$5.49

21=$4.75

Step-by-step explanation:trust me bro

Answer:

7 1/3

Step-by-step explanation:

Answer:

X=28

Step-by-step explanation:

Answer:

The sequence is recursive and can be represented by the function f(n + 1)= f(n) + 3/8

Step-by-step explanation:

i got it right on the assignment

Answer:

Solve the system of equations.

x = 1

y = 2

Step-by-step explanation:

Hope it is helpful....

\(5x + 2y = 9\)

with given condition where y = 2.

Therefore, substitute the value of y in the equation.

\(5x + 2(2) = 9 \\ 5x + 4 = 9\)

\(5x = 9 - 4 \\ 5x = 5 \\ x = \frac{5}{5} \longrightarrow \frac{1}{1} \\ x = 1\)

\(5x + 2y = 9 \\ 5(1) + 2(2) = 9 \\ 5 + 4 = 9 \\ 9 = 9 \longrightarrow \bf{true} \: \green{ \checkmark}\)

Hence, the value of x is 1.

\( \large{x = 1}\)

The sample size should be approximately 4704 to achieve a margin of error of 4 with a 95% confidence level from a population with a standard deviation of 35.

To achieve a margin of error of 4 with a 95% confidence level from a population with a standard deviation of 35, the sample size should be calculated using the formula for sample size determination in confidence intervals.

To determine the required sample size, we can use the formula:

n = \((Z \cdot \sigma / E)^2\)

where:

n = sample size

Z = Z-score corresponding to the desired confidence level (in this case, 95% confidence level)

σ = population standard deviation

E = margin of error

In this scenario, the margin of error (E) is 4, and the population standard deviation (σ) is 35.

We need to find the appropriate Z-score for a 95% confidence level.

The Z-score for a 95% confidence level is approximately 1.96.

Plugging in these values into the formula, we have:

n = \((1.96 \cdot 35 / 4)^2\)

Simplifying the equation, we get:

n = \((68.6)^2\)

n ≈ 4704

Therefore, the sample size should be approximately 4704 to achieve a margin of error of 4 with a 95% confidence level from a population with a standard deviation of 35.

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Answer:

The slope is 1/3

Step-by-step explanation:

To find the slope of a line, we can use two points and the slope formula

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

Picking two points on the line ( 0,2) and ( 3,3)

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

    = 1/3

The slope is 1/3

Answer:

She will not be correct

Step-by-step explanation:

Given data

Length=10in

Width=7in

Height=3in

The volume of the toolbox

V=10*7*3

V=210 in^3

Let us double the volume and see

2V= 210*2

   =420 in^3

Let us also double the individual dimensions

Length=20

Width=14in

Height=6in

V= 20*14*6

V=1680 in^3

Hence the volume will be different, she will not be correct

Answer:

x = 10

\( m\angle DCE=55\degree \)

Step-by-step explanation:

Since, CE bisects angle DCF, therefore:

\( m\angle ECF= m\angle DCE\)

\( 6x-5=4x + 15 \)

\( 6x-4x=5 + 15 \)

\( 2x=20 \)

\( x=\frac{20}{2} \)

\( x=10\)

\( m\angle DCE=(4x+15)\degree \)

\( m\angle DCE=(4\times 10+15)\degree \)

\( m\angle DCE=(40+15)\degree \)

\( m\angle DCE=55\degree \)

Answer  10x5

Step-by-step explanation:

The equation that can be used to find h, the number of hours Aaron can rent the bike, is: 15h + 3 = 65, where h represents the number of hours.

To find the number of hours Aaron can rent the bike, we need to consider the cost per hour and the additional fee for the helmet. The cost per hour is $15, and the additional fee for the helmet is a one-time payment of $3 for the entire ride.

Let's break down the equation step by step:

Cost per hour: 15h

Additional fee for the helmet: 3

The total cost of renting the bike for h hours, including the helmet fee, should be equal to Aaron's budget, which is $65.

Therefore, the equation becomes:

15h + 3 = 65

To find the value of h, we solve the equation:

15h = 65 - 3

15h = 62

h = 62/15

h ≈ 4.13

Aaron can rent the bike for approximately 4.13 hours. Since it's not possible to rent a bike for a fraction of an hour, Aaron would round down to the nearest whole number. Therefore, he can rent the bike for 4 hours.

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The volume of the square pyramid is  400 m³

The formula that is used for calculating the volume of a square pyramid is expressed as;

V = a²h/3

Such that the parameters of the given equation is;

From the information given in the diagram, we have that;

a , length of side = 10m

Height = 12m

Substitute the values, we have;

Volume = 10² × 12/3

Divide the values, we have;

Volume = 10² × 4

Find the square

Volume = 100 × 4

Multiply the values, we get;

Volume = 400 m³

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Answer:

56,52

Step-by-step explanation:

take n as 3.14 multiples with 9 and multiples with 2

Answer: b

Step-by-step explanation:

bc

Answer: A

Step-by-step explanation:

An experiment can show that all angles of a rectangle are equal and angles.

To verify experimentally that all angles of a rectangle are equal and right angles, you can perform the following steps:

Through these steps, you can verify experimentally that all angles of a rectangle are equal and right angles.

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An element is a pure material made up of atoms with the same amount of protons in their nuclei. The atomic number and the mass number of the element X are 92 and 238 respectively.

In chemistry, an element is a pure material made up of atoms with the same amount of protons in their nuclei. Chemical elements, unlike chemical compounds, cannot be broken down into simpler substances by any chemical process.

Let us consider, that z is the atomic no and A is the mass no of the parent element 'X'.

As per the question, X emits two successive alpha particles (²₁He) and one beta, i.e, particle and reached to daughter element (²³⁰₈₉Ac).

Now according to the question, we can write,

\(^A_ZX \overset{-\alpha}{\rightarrow}\ \ ^{A-4}_{Z-2}X\ +\ ^4_2He\ \ \overset{-\alpha}{\rightarrow}\ \ ^{A-8}_{Z-4}X\ +\ ^4_2He\ \ \overset{-\-\beta}{\rightarrow}\ \ ^{A-8}_{Z-3}X\ +\ ^0_{-1}He\)

We see, \(^A_ZX\) that after two α and one β of emission, we get the daughter element \(^{A-8}_{Z-3}X\). Again as given in the problem, the daughter element is \(^{230}_{89}AC\).

∴We can write-

\(^{A-8}_{Z-3}X=^{290}_{89}AC\)

comparing the two, we get,

Z-3=89

Z=92

A-8=230

A=238

Hence, the atomic number and the mass number of the element X is 92 and 238 respectively.

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Answer with Step-by-step explanation:

7x+x=90 [Being complementary angles]

8x=90

x=90/8

x=11.25

x-38+x=180 [Being supplementary angles]

2x=218

x=109

Centipedes differ from millipedes in that centipedes are cylindrical, have poison claws, and 2 pairs of appendages per body segment: FALSE

As it is given in the description, centipedes have only one pair of legs on each body segment. So, the whole statement becomes False.

Therefore, the statement "centipedes differ from millipedes in that centipedes are cylindrical, have poison claws, and 2 pairs of appendages per body segment" is FALSE.

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Complete question:

Centipedes differ from millipedes in that centipedes are cylindrical, have poison claws, and 2 pairs of appendages per body segment. TRUE or FALSE

x = (qp)/w                

Simplify and get x on one side of equation

Answer:

  the SSS similarity theorem

Step-by-step explanation:

The triangles are not indicated as being right triangles (even though we know they are), so we cannot use the HL theorem.

The ratios of corresponding sides are the same, so the applicable theorem is ...

  the SSS similarity theorem

__

3/(3+6) = 4/(4+8) = 5/15 = 1/3 . . . the ratio of shorter sides to corresponding longer sides.

_____

Additional comment

You recognize the smaller triangle as a 3-4-5 right triangle, and notice that the larger triangle is 3 times that size. If angle C were marked as the right angle it is, then the HL similarity theorem could also be used.

a) Let’s assume the regression equation as follows: log(wage)i = β0 + β1College_edui + β2Experiencei + β3Experiencei^2 + ui

Where:• i is the index of individuals• College_edui is a dummy variable, taking value 1 if an individual is a college graduate, and 0, otherwise•

Experience i is the experience of i th individual• Experiencei^2 captures the squared effect of experience (i.e. the non-linear effect of experience on wage).

b) Let’s denote the variable Top10i to take value 1 if ith individual is graduated from a top 10 university, and 0 otherwise. Then, the regression equation becomes:

log(wage)i = β0 + β1College_edui + β2Top10i + β3(College_edui x Top10i) + ui

Here,β3 is the wage gap between top 10 university graduates (Group 1) and non-top 10 university graduates (Group 2).The null hypothesis (H0): β3 = 0.The alternative hypothesis (H1): β3 ≠ 0.

c) Let the regression equation be:

log(wage)i = β0 + β1College_edui + β2Experiencei + β3Experiencei^2 + β4(College_edui x Experiencei) + ui.

The null hypothesis (H0): β4 = 0 (i.e. the return to college education does not vary with experience).The alternative hypothesis (H1): β4 ≠ 0 (i.e. the return to college education varies with experience).

d) The regression equation allowing the return to college education to vary with which university you graduate from is:

log(wage)i = β0 + β1College_edui + β2Top10i + β3(College_edui x Top10i) + ui.

Here, β3 is the wage gap between the two groups (top 10 universities and non-top 10 universities).

The null hypothesis (H0): β3 = 0 (i.e. the return to college education does not differ between the two groups).

The alternative hypothesis (H1): β3 ≠ 0 (i.e. the return to college education differs between the two groups).

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Answer:

Step-by-step explanation:

Vertically opposite angles are congruent.

∠A = ∠C

∠A + ∠C = 254

∠A + ∠A = 254

      2∠A = 254

        ∠A = 254/2

∠A = 127

Linear Pair: In two adjacent angles, if the non common arms are opposite  rays, then they are called linear and they add up to 180

∠A + ∠B = 180  {linear pair}

127 + ∠B = 180

        ∠B = 180- 127

        ∠B = 53°

Answer: 8 (2y-1)

Step-by-step explanation: first start by writing like this below:

16y-8

Then factorise the numbers(cut the numbers)

2×2×2×2×y - 2×2×2

Now take all which is common like:

2×2×2=8

Then,take the remained numbers and add it into the brackets.

8 (2y - 1) Here, why we should put 1,because there's nothing left.

If you want to check the answer, factorise this expression and see:

8 (2y-1)

16y-8.

Hope it helps you!!

The Probability of red light is 0.3

P(red) = 0.3

The probability that out of the next eight eastbound cars that arrive randomly at the light, exactly three will be stopped by a red light be 0.25.

P(exactly three get stopped by red light)=0.25

The correct option is (d) P(red)=.3,P(exactly 3 get stopped)=.25

A binomial distribution can be thought of as simply the probability of a SUCCESS or FAILURE outcome in an experiment or survey that is repeated multiple times.

The occurrence,

p= probability of a red light

 =\(\frac{15}{15+5+30}\)

 = \(\frac{15}{50}\)

 = 0.3

Hence, Probability of getting red light be,

P (red)= 0.3

Now, the Binomial distribution formula,

Probability=( \(_r^nC\))\(\;p^{r} \;q^{n-r}\)

where, r = number of times for a specific outcome within n trials

\(_r^nC\)   = number of combinations

p = probability of success on a single trial

q = probability of failure on a single trial

n = number of trial

According to question,

          = 1- 0.3

          = 0.7

Now using the formula, ( \(_r^nC\))\(\;p^{r} \;q^{n-r}\)

P( exactly 3  get stopped) = ( \(_3^8C\))\(\;(0.3)^{3} \;(0.7)^{8-3}\)

                                            = \(\frac{8!}{3!(8-3)!}\) \((0.027) \; (0.7)^{5}\)

                                           =  \(\frac{8!}{3!(5)!}\)\((0.027) \; (0.16807)\)

                                           = \(\frac{8 * 7 * 6 }{3 * 2}\) x 0.027 x 0.16807

                                           = 56 x 0.00453789

                                           = 0.25412184

                                          ≈ 0.25

Hence, Probability of next eight eastbound so that exactly three will stopped by a red light be 0.25.

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Both of Nick's bags weigh 41 kilograms combined.

In mathematical terms, if we let W1 be the weight of the first bag and W2 be the weight of the second bag, then the total weight of both bags can be expressed as W1 + W2.

Substituting the given values, we get:

Total weight of both bags = 24 + 17 = 41 kilograms.

This is a simple addition problem that involves adding the weights of two bags to find the total weight.

The complete question is:

Nick is going on vacation. one of his bags weighs 24 kilograms. the other bag weighs 17 kilograms. how much do both of nick's bags weigh combined?

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