Round 0.698 to nearest hundredth

Answer:

The probability that on any given day, there will be 9 individuals arriving at the food pantry is 0.1241

Step-by-step explanation:

Here, we are to use Poisson distribution probability formula

Please check attachment for detailed explanation

Answer:$8.43 each

Step-by-step explanation:

$13.86+$3.00=$16.86

$16.86➗2=$8.43

Answer:

8.43

Step-by-step explanation:

Answer:

3.47

Step-by-step explanation:

p varies inversely with q, so:

p = k/q, where k is a constant.

When q = 17, p = 10.

10 = k/17

k = 170

p = 170/q

When q = 49:

p = 170 / 49

p ≈ 3.47

Answer:

Purchase price = $412.94 (nearest cent)

Total price = $430.49 (nearest cent)

Step-by-step explanation:

Purchase price

If 4.25% = $17.55

⇒ 100% = (17.55 ÷ 4.25) × 100 = 412.9411765...

⇒ Purchase price = $412.94 (nearest cent)

Total price

total price = purchase price + sales tax

                 = $412.94 + $17.55

                 = $430.49

So let the original price be x

Total price:-

Answer: a. To find the slope and y-intercept of the linear equation, we need to write it in slope-intercept form (y = mx + b). To do this, we can add 10y to both sides and divide both sides by 10 to get:

y = -559x/10 - 2701/10

y = -55.9x - 270.1

The slope of the equation is -55.9, and the y-intercept is -270.1

b. The slope of a linear equation is the rate of change of the dependent variable (y) with respect to the independent variable (x). In this context, the slope of -55.9 means that for every year after 2012, the number of people employed as registered nurses is expected to decrease by 55.9 thousand.

c. The y-intercept of a linear equation is the point where the line crosses the y-axis. In this context, the y-intercept of -270.1 means that in 2012, there were expected to be 270.1 thousand people employed as registered nurses.

Step-by-step explanation:

The probability of caterpillar hitting only blue boxes instead of red box or taking other route is 1/2. It means there are 50% chances of caterpillar to hit blue box

The likelihood that an event will occur is defined by probability. In many instances in real life, we may need to make predictions about how something will turn out. Our certainty about an event's outcome may be high or low. In such circumstances, we refer to the likelihood that the event will take place. Generally speaking, probability has many useful uses in games, business (to make forecasts based on probability), and this emerging branch of artificial intelligence.

Suppose, the number of red box are 5

                the number of blue boxes are 7

                number of escape routes are 2

probability = no. of favorable event / total no. of events

probability of caterpillar hitting the blue box = 7/ 14

                                                                           = 1/2

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The volume of a cone is computed as follows:

where r is the radius and h is the height

Replacing with data and solving for r:

Hello!

-4(-5 + 3)

= -4(-2)

Answer:

C

Step-by-step explanation:

-4(-5+3)
20+(-12)

The surface area of a rectangular prism is 48 5/6 mi².

In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:

Surface area of a rectangular prism = 2(LH + LW + WH)

Where:

By substituting the given side lengths into the formula for the surface area of a rectangular prism, we have the following;

Surface area of rectangular prism = 2[6 × 2 1/3 + (1 1/4 × 6) + (1 1/4 × 2 1 /3)]

Surface area of rectangular prism = 2[14 + 15/2 + 35/12]

Surface area of rectangular prism = 48 5/6 mi².

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Answer:

y=1/4x+6

Step-by-step explanation:

The formula for writing a slope equation is y=mx+b. The slope is 1/4, or m, and the y-intercept is 6, or b. Don't worry about the x or y, leave them as variables.

Using proportions, it is found that her new balance after she makes one new transaction for $351 is of $3,861.

A proportion is a fraction of a total amount.

Rae's unpaid credit card balance was $3,744, then considering the APR of 12.5%, when she makes the payment it will be 112.5% of that, that is:

B = 1.125 x 3744 = $4,212.

Considering the payment of $351:

4212 - 351 = $3,861.

Her new balance after she makes one new transaction for $351 is of $3,861.

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The correct illustration of plotting the points is attached in the image.

few of the points are (2, - 1), (3, 1), (4, 3), and (5, 5).

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

From the given information first, we plot a point (1, - 3) on the x-y coordinate.

Plotting more points by moving up 2 and right 1 would be, (x + 1, y + 2).

So, Some of such points are,

(2, - 1), (3, 1), (4, 3), and (5, 5).

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Answer:

5 meters : 1 gallon

fuel efficiency of Car is 7 meters per gallons

Step-by-step explanation:

Given Tanya car goes 45 meters on 7 gallons.

In terms of ratio  of distance traveled and fuel consumed

45 meters : 7 gallons

since both 45 and 7 are multiple of 7 dividing both side by 7

45/7 meters : 7/7 gallons

5 meters : 1 gallon

Thus, fuel efficiency of Car is 7 meters per gallons.

Answer:

A. The kinetic energy is quartered.

Step-by-step explanation:

Using the t-distribution, it is found that since the p-value of the test is 0.72 > 0.05, there is not significant difference between the values of each group.

At the null hypothesis, we test if the groups have the same values, that is, the subtraction of their means is 0:

\(H_0: \mu_2 - \mu_1 = 0\)

At the alternative hypothesis, we test if the groups have different values, that is, the subtraction of their means is different of 0:

\(H_1: \mu_2 - \mu_1 \neq 0\)

First, we have to find the mean and the standard deviation for both samples, hence, using a calculator:

\(\mu_1 = 18.75, \sigma_1 = 6.2507, \mu_2 = 19.75, \sigma_2 = 4.2678\)

The standard errors are:

\(s_1 = \frac{\sigma_1}{\sqrt{n_1}} = \frac{6.2507}{\sqrt{8}} = 2.21\)

\(s_2 = \frac{\sigma_2}{\sqrt{n_2}} = \frac{4.2678}{\sqrt{8}} = 1.5089\)

For the distribution of differences, we have that:

\(\overline{x} = \mu_2 - \mu_1 = 19.75 - 18.75 = 1\)

\(s = \sqrt{s_1^2 + s_2^2} = \sqrt{2.21^2 + 1.5089^2} = 2.676\)

We have the standard deviation for the samples, hence, the t-distribution is used. The test statistic is given by:

\(t = \frac{\overline{x} - \mu}{s}\)

In which \(\mu\) is the value tested at the null hypothesis, which is 0 for this problem. Hence, the value of the test statistic is:

\(t = \frac{\overline{x} - \mu}{s}\)

\(t = \frac{1 - 0}{2.676}\)

\(t = 0.37\)

To find the p-value, we have a two-tailed test, as we test if the means are different from a value, with t = 0.37 and 8 + 8 - 2 = 14 df.

Using a t-distribution calculator, this p-value is of 0.72.

Since the p-value of the test is 0.72 > 0.05, there is not significant difference between the values of each group.

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Let \(x\) and \(y\) be the amounts of available alloy (AA) and pure magic steel that are used, so we also have

\(x + y = 2.7\)

DA13 is supposed to contain 7% gold, 3% silver, and 90% steel, so that 2.7 kg of it is made up of

\(0.07 \times 2.7 \,\mathrm{kg} = 0.189 \,\mathrm{kg} \text{ gold}\)

\(0.03 \times 2.7 \,\mathrm{kg} = 0.081 \,\mathrm{kg} \text{ silver}\)

\(0.90 \times 2.7 \,\mathrm{kg} = 2.43 \,\mathrm{kg} \text{ magic steel}\)

For each kg of the available alloy (AA), there is a contribution of 0.21 kg of gold, 0.09 kg of silver, and therefore 0.70 kg of steel; \(x\) kg of it will contain \(0.21x\) kg of gold, \(0.09x\) kg of silver, and \(0.70x\) kg of steel. Each kg of magic steel of course contributes 1 kg of steel; \(y\) kg of it will contribute \(y\) kg of steel.

Then the dwarves need

• total gold: \(0.21x = 0.189\)

• total silver: \(0.09x = 0.081\)

• total steel: \(0.70x + y = 2.43\)

Solve for \(x\) and \(y\). The first two equations are consistent and give \(x = 0.90\), and substituting this into the third we find \(y = 1.80\). So the dwarves must combine 0.90 kg of AA and 1.80 kg of magic steel.

The bearing from the phone to the transmitter is approximately 31 degrees to the east of the north direction.

To determine the bearing from the phone to the transmitter, we can use trigonometry.

The bearing is typically measured clockwise from the north direction.

Given that the transmitter is 13 km west and 21 km south of the phone, we can form a right triangle with the phone as the vertex angle.

The side opposite to the vertex angle represents the north-south direction, and the side adjacent to the vertex angle represents the east-west direction.

Using the tangent function, we can calculate the angle:

tangent(angle) = (opposite side) / (adjacent side)

tangent(angle) = 21 km / 13 km

Taking the inverse tangent (arctan) of both sides, we find:

angle = arctan(21 km / 13 km)

Evaluating this using a calculator, we find the angle to be approximately 58.57 degrees.

However, since the bearing is measured clockwise from the north, we need to subtract this angle from 90 degrees (which represents the north direction) to obtain the bearing:

bearing = 90 degrees - 58.57 degrees

Calculating this, we find the bearing to be approximately 31.43 degrees.

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The length FE in the circle is 6 units

The arc AE has a measure of 64 degrees

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

The circle

Given that the lengths from the center to either chords are equal

This means that

FE = 6 units

For the other circle, we have

BC = 58 degrees

AB = ED

The arc AE is calculated as

AE = 180 - BC - ED

Where

AB = ED = BC = 58 degrees

So, we have

AE = 180 - 58 - 58

Evaluate

AE = 64

Hence, the arc AE is 64 degrees

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Answer:

4.2.1)  R140 000

4.2.2)  R144 758.28

4.2.3)  Option 2

Step-by-step explanation:

To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000 \cdot 0.12 \cdot 6\)

\(I=24000 \cdot 6\)

\(I=144000\)

Therefore, the return on Ayanda's investment using Option 1 is R144000.

\(\hrulefill\)

To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000(1+0.095)^6-200000\)

\(I=200000(1.095)^6-200000\)

\(I=200000(1.72379142...)-200000\)

\(I=344758.28426...-200000\)

\(I=144758.28426...\)

\(I=144758.28\)

Therefore, the return on Ayanda's investment using Option 2 is R144758.28.

\(\hrulefill\)

Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.

Answer:

\(D = 72.2\ yd\)

Step-by-step explanation:

Given

\(Length\ (L)= 58\ yd\)

\(Width \ (W)= 43\ yd\)

Required

Determine the diagonal (D)

The relationship between D, L and W can be gotten using Pythagoras Theorem:

\(D^2 = L^2 + W^2\)

Substitute values for L and W

\(D^2 = 58^2 + 43^2\)

\(D^2 = 3364 + 1849\)

\(D^2 = 5213\)

Take Square root of both sides

\(D = \sqrt{5213}\)

\(D = 72.2011080247\)

\(D = 72.2\ yd\) (Approximated)

Answer:

point A is located at (3,9)

point D is located at (9,3)

point B is located at (6,5)

point C is located at (5,6)

Step-by-step explanation:

Answer:

-2.4+3.2t

Step-by-step explanation:

\(-3.6-1.9t+1.2+5.1t\\\\=(-3.6+1.2)+(-1.9+5.1)t\\\\=-2.4+3.2t\)

Answer:

-2.4+3.2t

Step-by-step explanation:

Khan

Answer:

d) 1/12

Step-by-step explanation:

Answer:

-9/5 or -1.8

Step-by-step explanation:

3x+27=-2x+18 add 2x to both side

5x+27=18 minus 27 from both side

5x=-9 divide 5

x=-9/5, in decimal form=-1.8

Answer:-9/5

Step-by-step explanation:

3x + 27 = -2x + 18

    -27           -27

-3x = -2x - 9

+2x   +2x

5x = -9

5x/5 = -9/5

x= -9/5                

6. x=100

7.x=75

8.x=30

10.x=112

11.x=58 y=58

Answer:

6) x = 70°

7) x = 75°

8) x = 30°

10) x = 112°

11) x = 58° , y = 58°

Step-by-step explanation:

6) two congruent sides means two congruent angles

   x + x + 40 = 180         2x = 140

7) two congruent sides means two congruent angles

   both base angles measure 75 degrees

8) isosceles triangle (has two equal sides)   75(2) + x = 180    150 + x = 180

10)  two congruent angles means two congruent sides

      44 + 2n = 180      2n = 136      n = 68

      angles n and x form a linear pair and equal 180

      180 - 68 = 112

11) isosceles triangle so ∡x = ∡y   64 + x + x = 180

   64 + 2x = 180      2x = 116        x = 58

Answer:

a) 0.1536 = 15.36% probability that exactly two of the four components last longer than 1000 hours.

b) 0.9728 = 97.28% probability that the subsystem operates longer than 1000 hours.

Step-by-step explanation:

For each component, there are only two possible outcomes. Either they fail in less than 1000 hours, or they do not. The probability of a component failing in less than 1000 hours is independent of any other component. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

One subsystem has four identical components, each with a probability of 0.2 of failing in less than 1000 hours.

Four components means that \(n = 4\)

Probability of 0.2 of failling means that 1 - 0.2 = 0.8 probability of not failling, so \(p = 0.8\)

a) Find the probability that exactly two of the four components last longer than 1000 hours.

This is \(P(X = 2)\). So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 2) = C_{4,2}.(0.8)^{2}.(0.2)^{2} = 0.1536\)

0.1536 = 15.36% probability that exactly two of the four components last longer than 1000 hours.

b) Find the probability that the subsystem operates longer than 1000 hours.

It will operate if at least two compoents last longer than 1000 hours. So

\(P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4)\)

In which

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 2) = C_{4,2}.(0.8)^{2}.(0.2)^{2} = 0.1536\)

\(P(X = 3) = C_{4,3}.(0.8)^{3}.(0.2)^{1} = 0.4096\)

\(P(X = 4) = C_{4,4}.(0.8)^{4}.(0.2)^{0} = 0.4096\)

\(P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.1536 + 0.4096 + 0.4096 = 0.9728\)

0.9728 = 97.28% probability that the subsystem operates longer than 1000 hours.

The length of segment A.F in the circles given is: 62 units.

A radius of a circle is half the diameter of a circle, which is a point from the center to any point on the circumference of the circle. This implies that any segment that is drawn from the center of a circle to any point on the circumference of a circle is a radius. Also, all radii of a circle are always congruent to each other.

Radius of circle B = AB = BD = 24 units [all radii of a circle are congruent to each other].

Radius of circle E = CE = EF = 9 units [all radii of a circle are congruent to each other].

CD = 4

DE = x

CD + DE = CE

Plug in the values into the equation

4 + x = 9

x = 9 - 4

x = 5

DE = 5

The length of segment DE is 5 units

A.F = AB + BD + DE + EF

Plug in the values into the equation

A.F = 24 + 24 + 5 + 9

A.F = 62 units.

Therefore, the length of segment A.F in the given circle is determined as: 62 units.

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