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Note * Use the d=rt formula (distance = rate * time). NOTE: You may not be able to solve for the variable. If you do not have enough information to solve for the variable then write the equation.

1) 50 mph

2) 70 mph

3) x mph

4) (x+10)mph

5) (x-5)mph

Using the normal distribution, the probability is given as follows:

P(x≤81) = 0.0158.

Since this probability is very small, less than 0.05, it suggest that the media reports overstated the proportion of cellphone users that developed cancer.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, the proportion and the sample size are given by:

p = 0.000412, n = 250178

Hence the mean and the standard deviation for the approximation are given by:

The probability that x is of 81 or less than the p-value of Z when X = 81.5, accounting for continuity correction, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{81.5 - 103.1}{10.15}[/tex]

Z = -2.13

Z = -2.13 has a p-value of 0.0158.

Hence:

P(x≤81) = 0.0158.

Since this probability is very small, less than 0.05, it suggest that the media reports overstated the proportion of cellphone users that developed cancer.

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Answer: 10204 millimeters

Step-by-step explanation: A gallon = 3875 mm. A quart is 946. 946x 3 = 2838. A pint is around 473 mm which, when multiplied by 7, is 3311. Finally, there are 6 ounces which are approximately 30 mm. 6x30 = 180. We add all of this up : 3875 + 2838+ 3311 + 180 = 10204.

The future value interest earned semiannually at a  compound rate of 4% is $7598.89.

To calculate the future value in interest earned, we use the of compound interest

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

Formula:

Where:

From the question,

Given:

Substitute the values above into equation 1

Hence, the future value interest earned is $7598.89.

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Answer:

7.88 x 10^5 is 788,000 is scientific notation

Answer:

2 1/8

Step-by-step explanation:

I counted from 29 to 31 and then saw that for 29 it was 3/8 and for 31 it was 2/8 so i knew that the answer would be 2 1/8

P11 equals  769.417 and general formula is 19*(1.4)^(n)

Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself

The growth rate is .4 per time period.

the exponential growth model is f = p * (1 + .4) ^ n

f is the future value.

p is the present value.

r is the growth rate per time period.

n is the number of time periods.

in p0, n = 0

in p11, n = 11

you are given that p0 = 19

in the formula, that becomes f = 19 * (1 + .4) ^ 0 = 19 * (1.4) ^ 0 = 19.

the formula for p1 becomes f = 19 * (1 + .4) ^ 1 = 19 * (1.4) ^ 1 = 26.6

the formula for p11 becomes f = 19 * (1 + .4) ^ 11 = 19 * (1.4) ^ 11 = 769.417

the formula for pn becomes = 19*(1.4)^(n)

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Answer:

84

Step-by-step explanation:

Since we are given line OP perpendicular to line DR, then angles PDR and ODR are right angles.

Angles PDA and ADR are complementary.

Angles ODU and UDR are complementary.

Angles ADR and UDR are given as congruent.

We can conclude that angles PDA and ODU are congruent.

By AA Similarity, triangles APD and UMD are similar.

DP/DM = PA/MU

3.75/10 = 4.5/MU

3.75MU = 10 × 4.5

MU = 12 (altitude of triangle DUO)

OD = OM + MD =  4 + 10 = 14 (base of triangle DUO)

area = base × height / 2

area = 14 × 12 / 2

area = 84

Answer:

84

Step-by-step explanation:

correct me if im wrong

The effect of  Edible a portion Price on your profit margin , if we only use the as purchased price to determine our cost and selling price is that it will maximize the profit because it will account for every part of the production.

The portion cost can be calculated by multiplying the cost of a usable kg  with the  portion size.

This can be represented as : portion cost = (portion size x cost of usable kg)

It should be noted that Edible portion (EP)  serves as the  portion of food  which will be given top the   customer after  the preparation.

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Answer:

Step-by-step explanation:

The inequality that compares the number of videos Sarita uploaded, v, to the number of videos Tyson uploaded is v - 500 < y

Inequality for number of videos Sarita uploaded:

v - 500 < y

Therefore, the inequality that compares the number of videos Sarita uploaded, v, to the number of videos Tyson uploaded is v - 500 < y

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Answer:

- v < 500

Step-by-step explanation:

Answer:

five-hundredths

Step-by-step explanation:

The major requirements for a group of individuals and organisations to be a market as evident from the definition big a market is that; there must be an exchange of goods or services in which case, there are sellers and buyers.

The occurrence of the exchange of goods and services represents the qualifying requirement for a market.

The distinctive property between a consumer market and a business-to-business market is the that former, involves the end user of the good or service while the latter involves the use of the good or service exchanged to facilitate the production of other goods.

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a. Central angle in the circle is: Angle BAC

b. A major arc is: Arc BEC

c. A minor arc is: Arc BC

d. measure of arc BEC is: 260°

e. m(BC) = 100°

A central angle has two of its sides as radii of the circle, forming an angle at the center of the circle, where the vertex is at the center of the circle.

A major arc has a measure that is greater than 180 degrees. That is, it is more than half a circle (semicircle). Thus, measure of major arc > 180 degrees.

A minor arc has a measure that is less than 180 degrees. That is, it is not more than half a circle (semicircle). Thus, measure of minor arc < 180 degrees.

a. Central angle in the circle is: Angle BAC

b. A major arc in circle A is: Arc BEC

c. A major arc in circle A is: Arc BC.

d. Measure of arc BEC = 360 - 100 [according to the central angle theorem]

Measure of arc BEC = 260°.

e. Measure of angle BAC = 100°  [given]

Measure of arc BC = angle BAC [according to the central angle theorem]

Measure of arc BC = 100°

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The cosine equation of the attached graph is; y = 5 cos [( π/40)(x - (π/2))] + 3

The given parameters are:

Diameter = 10 m

Thus;

Radius; r = 5 m

Time; t = 80 s

Height above the ground, h = 2 m

The above means that:

Amplitude; A = 5 m

Period, T = 80 s

Minimum = 2 m

The cosine function is represented as:

y = a cos [k(x - d)] + c.

where;

A is amplitude

B is cycles from 0 to 2π

period = 2π/k

d is horizontal shift

c is vertical shift (displacement)

Thus;

2π/k = 80

k = 2π/80 = π/40

Where

c = Amplitude - Minimum

c = 5 - 2

c = 3

Shift to the left by π/2 gives;

d = π/2

Thus, the equation of the cosine graph is;

y = 5 cos [( π/40)(x - (π/2))] + 3

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Answer:

a) (1,6 x 150)/100 = 2,4 dollars

b) (11,3 x 950)/100 = 107,35 dollars

c) (0,29 x 2000)/100 = 5,8 dollars

Answer:

69500

Step-by-step explanation:

695 x 100 = 69500

to check answer divided 69500 by 100

which is equals to 695

695 is a hundred times smaller than 69500

multiplication is a method of finding the product of two or more numbers.

We need to find the number which 695 is a hundred times smaller than

Six hundred ninety five times smaller than

Let us consider the number to be x.

Let us multiply 695 with 100 to  get the value or answer of the above question.

Six hundred ninety five into hundred is sixty nine thousand five hundred

695 x 100 = 69500

To verify the answer is correct or not , divide 69500 by 100. if we get 695 out answer is correct

69500/100=695

Hence 695 is a hundred times smaller than 69500

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Answer:

angle G

Step-by-step explanation:

the quadrilateral did not change position or ration, it only shrank, so all the angles are in the same place and angle C = angle G

Answer:

2

Step-by-step explanation:

Answer:

Step-by-step explanation:

add both the equations then you will get

3x^3-x^2+2

but in the standard form there should be an x^1 term or x term since there is no term like that we write it as 0x

so the equation will be

3x^3-x^2+0x+2

The points would be matched with their polar coordinates as follows:

A polar coordinate can be defined as a two-dimensional coordinate system, wherein each point on a plane is typically determined by a distance (r) from the pole (origin) and an angle (θ) from a reference direction (polar axis).

In geometry, the relationship between a polar coordinate (r, θ) and a rectangular coordinate (x, y) based on the conversion rules is given by the following polar functions:

a = rcos(θ)    ....equation 1.

b = rsin(θ)     ....equation 2.

Where:

In Mathematics, a negative vector for a given vector has the same magnitude but acts in an opposite direction while an antiparallel vector for a given vector refers to any vector that acts in an opposite direction.

This ultimately implies that, a negative vector equals to an antiparallel vector, but an antiparallel vector isn't always a negative vector.

In this context, we can infer and logically deduce that the points would be matched with their polar coordinates as follows:

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Two or more triangles are congruent if on comparison, they have equal lengths of sides, and measure of angles.

Therefore, the required proofs for each question are shown below:

Problem 1:

Congruent triangles are triangles with equal lengths of corresponding sides and measures of internal angles.

Thus,

                     STATEMENT                          REASON

1. <NMQ ≅ <NPQ                            Any point on a perpendicular bisector      

                                                        makes equal measure of angle with the

                                                        two ends of the line segment.

2. NQ ⊥ MP                                     Definition of a line.

3. MQ ≅ PQ                                     Equal segments of a bisected line.

4. MN ≅ PN                                     Any point on a perpendicular bisector    

                                                        is at the same distance to the

                                                        two ends of the line segment.

5. <MNQ ≅ <PNQ                           Equal measure of the bisected angle.

Problem 2:

A line segment is the shortest distance between two points.

            STATEMENTS                    REASONS

1. m<PSR  ≅ m<PSQ                A perpendicular bisector is always at a right  

                                                  angle to the bisected line segment.

2. m<RPS ≅ m<QPS                 Equal measure of the bisected angle.

3. RS ≅ QS                                Property of a bisected line segment.

4. PR ≅ PQ                                Any point on a perpendicular bisector    

                                                  is at the same distance to the two ends of  

                                                 the line segment.

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Answer:

Step-by-step explanation:

d

Answer:

76 sodas

Step-by-step explanation:

152 divided by 2

Answer: 76 sodas

Step-by-step explanation:

To find the sodas, use the data you see. Bottles of water are twice the sodas. So divided water by 2 to get the sodas.
152 ÷ 2 = 76 ( sodas ) . Hope it helps !

The odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly is 3.76.

An odds ratio is a measure of the strength of an association with the exposure and outcome.

The odds ratio can be calculated by dividing the odds of the first group (exposure) by the odds of the second group (outcome).

                             Flies      Does not fly     Total

Long beak               11               7                     19

Not a long beak      3              13                     15

Total                       14             20                    34

Probability of long beaks flying = 0.79 (1/14)

Probability of not having long beaks flying = 0.21 (3/14)

Odds ratio = 3.76 (0.79/0.21)

Thus, the odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly is 3.76, showing greater odds of association.

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Complete question

Researchers wanted to study if having a long beak is related to flight in birds. They surveyed a total of 34 birds. The data are shown in the contingency table below. What is the odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly? Round your answer to two decimal places.

Long beakNot a long beakTotalFlies11719Does not fly31315Total142034

By testing the hypothesis we can conclude that the bag does not contain 11 kg of food.

Given mean of 10.6 kg, population standard deviation of 0.6 and sample size of 25.

We are required to find whether the company is right in saying that their bags contain 11 kg of food.

First we have to make hypothesis.

[tex]H_{0}[/tex]:μ≠11

[tex]H_{1}[/tex]:μ=11

We have to use t statistic because the sample size is less than 30.

t=(X-μ)/s/[tex]\sqrt{n}[/tex]

We will use s/[tex]\sqrt{n}[/tex]=0.6 because we have already given population standard deviation of weights.

t=(11-10.6)/0.6

=0.4/0.6

=0.667

Degree of freedom=n-1

=25-1

=24

T critical at 0.05 with degree of freedom 24=2.0639

T critical at 0.05 with degree of freedom is greater than calculated t so we will accept the null hypothesis.It concludes that the bags donot contain 11 kg of food.

Hence by testing the hypothesis we can conclude that the bag does not contain 11 kg of food.

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By the definition and properties of absolute value, there are two possible resulting functions: (i) g(x) = 5 · |x|, (ii) g(x) = |5 · x|. (Correct choices: B, D)

Herein we must modify a parent function to get a resulting function by the use of rigid transformations, defined as those transformations applied on geometric loci, including functions, such that Euclidean distance is conserved.

Based on the statement seen in the picture, the enlargement of the parent function can be done by a rigid transformation known as dilation, whose definition is shown below:

g(x) = k · f(x), where k is the stretch factor and is greater than 1.     (1)

If we know that f(x) = |x| and k = 5, then the resulting function is:

g(x) = 5 · |x|     (1)

This expression is also equivalent to the expression g(x) = |5 · x| by definition of absolute value.

By the definition and properties of absolute value, there are two possible resulting functions: (i) g(x) = 5 · |x|, (ii) g(x) = |5 · x|. (Correct choices: B, D)

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Answer: Same

Step-by-step explanation:

Given formula

[tex]Percent~of~change~=~\Large\frac{New~-~Original}{Original}*100\%[/tex]

Given information

Troop A:

Troop B:

Substitute values into the formula (Troop A)

[tex]Percent~of~change~=~\Large\frac{New~-~Original}{Original}*100\%[/tex]

[tex]Percent~of~change~=~\Large\frac{(16)~-~(14)}{(14)}*100\%[/tex]

Simplify the fraction

[tex]Percent~of~change~=~\Large\frac{2}{14}*100\%[/tex]

[tex]Percent~of~change~=~\Large\frac{1}{7}*100\%[/tex]

[tex]Percent~of~change~\approx~14.29\%[/tex]

Substitute values into the formula (Troop B)

[tex]Percent~of~change~=~\Large\frac{New~-~Original}{Original}*100\%[/tex]

[tex]Percent~of~change~=~\Large\frac{(24)~-~(21)}{(21)}*100\%[/tex]

Simplify the fraction

[tex]Percent~of~change~=~\Large\frac{3}{21}*100\%[/tex]

[tex]Percent~of~change~=~\Large\frac{1}{7}*100\%[/tex]

[tex]Percent~of~change~\approx~14.29\%[/tex]

Compare the two percent of change

[tex]Troop~A~v.s.~Troop~B[/tex]

[tex]14.29\%~=~14.29\%[/tex]

Therefore, they are [tex]\Large\boxed{Same}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The answer is same.

Finding the percentage of change for Troop A :

New - Original / Original × 100%

Finding the percentage of change for Troop B :

Both the troops have the same percent change in membership.

The fraction of his farm which isn’t ruined is 11/18

Fractions are written as a ratio of two integers. The given question will be solved using the method of proportion.

If Uncle Bill has planted fruits in the farm and 7/12 is watermelon, and 2/3 of the watermelon section is ruined from the storm, the fraction ruined from the storm is;

Fraction ruined from the storm = 2/3* (7/12)

Simplify to its lowest term to have:

Fraction ruined from the storm = 7/18

Determine the fraction of the firm that is not ruined

Fraction not ruined = 1 - 7/18

Fraction not ruined = 11/18

Hence the fraction of his farm which isn’t ruined is 11/18 if uncle Bill has planted fruits in the farm and 7/12 is watermelon.

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Answer:

c

Step-by-step explanation:

consider points (0,2) and (-4,0)

slope=(0-2)/(-4-0)=-2/-4=1/2

y-intercept=2

y=mx+c

y=1/2 x+2

Answer:

y=1/2x+2

Step-by-step explanation: