Darwin's age is 6 years greater than twice fiona's age.If darwin is 50 years old, how many years old is fiona

The coordinates are the best estimate of the solution to the system of equations (-1,0). The correct option is A.

A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

The system of equations is,

-3x + y = 2

-4x + 7y = 1

When the graph is plotted on the coordinates axes, The value of x and y are -0.765 and -0.964, The best estimation for the coordinates will be (-1,0).

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When we have a biased dice where 3 comes up twice as often as each other number, the expected sum of the numbers that appears on two such dice is 48/7.

Therefore, the answer is (A) 48/7.

From given condition of bias, probability of getting 3 is

P(3) = 2 × p

where P(1) = P(2) = P(4) = P(5) = P(6) = p

We also know P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1

That is 2p + 5p = 1

p = 1/ 7

P(3) = 2/7

Expected sum of the numbers that appear on a dice can be obtained by

EV = 1×1/7 + 2×1/7 + 3×2/7 + 4×1/7 + 5×1/7 + 6×1/7

EV = 24/7

Expected sum of the numbers that appear on two dice can be obtained by twice of one dice that is

EV = 2×24/7

EV = 48/7

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The rectangle PQMN to rectangle RSTU and triangle XYZ to triangle ABC are congruent figures.

What are congruent figures?

Two figures are said to be 'congruent' if they can be placed exactly over each other. When you place one slice of bread on top of the other, you'll notice that they're both the same shape and size. The term "congruent" refers to having exactly the same shape and size.

To identify the congruent figures in the given figures:

Two polygons are congruent if they have the same size and same shape.

(1) Rectangle PQMN and rectangle RSTU are the same shapes.

MN ≅ RS

NP ≅ ST

QP ≅ UT

MQ ≅ UR

Therefore rectangle PQMN and rectangle RSTU are congruent figures.

(2) Triangle XYZ and triangle ABC:

XY ≅ AB

YZ ≅ BC

XZ ≅ AC

Therefore triangle XYZ and triangle ABC are congruent figures.

Hence, the rectangle PQMN to rectangle RSTU and triangle XYZ to triangle ABC are congruent figures.

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Based on the definition of similar solids, the value of x would be: D. 31.

Similar solids are defined as two solids that have proportional corresponding linear measures, which means the ratio of their linear measures are equal.

Examples of linear measures include height, length, width, circumference or radii. This means that, if two cylinders for example are similar, then the ratios of their radii or heights will be equal or proportional to each other.

The two solids are similar as stated in the image above, which means their corresponding linear measures will have ratios that are equal or they are proportional.

The linear measures here are the sides of the base of the solids. Therefore, the ratios would be:

29/14.5 = x/15.5

(14.5)(x) = (29)(15.5)

x = (29 × 15.5) / 14.5

x = 31

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Analysis of weekly widget production reveals that the number of widgets X produced in a week is a random variable with mean and standard deviation the mean and the standard deviation of C  is Third one.

Whats is a widget?

On both Apple iOS and Android devices, widgets present specific data that resides in an application running in the device. Each widget on an iPhone or other smartphone display presents selected bits of information that reside in the associated applications.

To add a widget on an Android smartphone, go to your home screen, touch and hold an empty space, then:

Tap Widgets. You'll see a list of what's available to install.

Touch and hold a widget. You'll see images of your home screens.

Slide the widget to where you want it. Lift your finger

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Answer:

Below

Step-by-step explanation:

Not very good syntax on your post

  I will assume   23.6 %  ow what numer is 45,400

       23.6 % = .236 in decimal

                 .236 * x  = 45400

                        x =  45400/ .236 = 192,372.8814

Answer:i believe its 60 with x=30

Step-by-step explanation:

Step-by-step explanation:

M(<BAC)=95° , M(<ABC)=2x , M(<ACD)=145°

let M(<ACB)=y

Then M(<ACB)+M(<ACD)=180° , Because they are in a straight line and straight line can measure 180°.

so , y+145°=180°

y=180°_145°

y=35° , M(<ACB)=35°

The sum.of the interior angle of any triangle is 180° . so now we have 95° , 38° and 2x so the value of x be

95°+35°+2x =180°

130°+2x=180°

2x=180°_130°

2x=50° , divide both sides by 2 to find the value of x

x=25° , 2*25°=50° , M(<ABC)=50°

M(<BAC)=95°, M(<ABC)=50° , M(<ACB) =35°

95°+50°+35°=180°

This is short. And it is does not have a binomial distribution.

Given,

When a variable has only two possible outcomes and each trial is independent of the others, the binomial distribution is utilised.

Here,

Yes, there are only two possible outcomes for each kid. Their last names either have more than six letters, or they do not.

However, as you choose, the names are not put back into the hat, changing the probabilities. As a result, the trials are not independent, and the distribution is not binomial.

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Answer:

(XYZ) and (ABC)

(MNQP) and (RUTS)

Step-by-step explanation:

XYZ and ABC are the same triangle. They are just rotated.

Similarly, MNQP and RUTS are the same figures. They are rotated.

Answer:

15wz² - 2wz³

Step-by-step explanation:

when collecting like terms the terms must have the same variables, with variables having the same exponents.

(15wz² + 3wz³) - 5wz³ ← remove parenthesis

= 15wz² + 3wz³ - 5wz³ ← collect like terms

= 15wz² + (3wz³ - 5wz³)

= 15wz² + (- 2wz³)

= 15wz² - 2wz³

Answer:

500

Step-by-step explanation:

We know that in one hour, there is 60 minutes. If we need to figure out how many pens are produced in two hours, we can use an equation that looks like this:

60 × 2 (number of hours) = 120 (total minutes)

Now that we know that 120 is the total amount of minutes, we now need to figure out how many pens are produced. If 50 pens are produced every 12 minutes, then we need to figure out how many times 12 goes into 120.

12 × 10 = 120

Now that we know that 12 goes into 120 10 times, we now need to multiply 10 by 50 to get the total amount of pens produced.

10 × 50 = 500

500 pens are produced every two hours,

Answer:

Step-by-step explanation:

A machine can manufacture 50 pens in 12 minutes. How many pens can it manufacture in two hours?

50 : 12 = x : 120

x = 50 × 120 : 12

x = 500

-------------------

check

50 : 12 = 500 : 120

25 : 6 = 25 : 6

25/6 = 25/6

the answer is good

Answer:

101000 centimeters

Step-by-step explanation:

The perimeter is the sum of the lengths of the sides. Thus, the perimeter is [tex]18167+39412+43812 \approx 101000[/tex]

Answer:

10

Step-by-step explanation:

56 ÷ 7 = 8 each.

80 ÷ 8 = 10

The number of  mac and cheese Abdullah can buy for $20 is 8.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, at the grocery store, Abdullah purchased 3 pounds of mac and cheese for $7.50.

Now, cost of 1 pound of mac and cheese =Total cost/Number of pounds of mac and cheese

= 7.50/3

= $2.50

Then, with $20 Abdullah can by =20/2.50

= 8

Therefore, the number of  mac and cheese Abdullah can buy for $20 is 8.

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Answer:

Step-by-step explanation:

i know this isnt the answer but see if this problem can be a guide to find the answer;/

Answer:

(7,6)

Step-by-step explanation:

An ordered pair is a member of both equations if it satisfies both equations. In other words, we need to find values of x and y that make both equations true.

We can start by setting the two equations equal to each other, since they both represent the same variable, x. This gives us the equation -5y + 37 = -6y + 43. We can then solve this equation by subtracting -6y from both sides, which yields -5y + 37 - (-6y) = -6y + 43 - (-6y), or -5y - (-6y) + 37 = 43. This simplifies to -y + 37 = 43, or y = 43 - 37 = <<43-37=6>>6.

Now that we have found the value of y that satisfies both equations, we can plug this value into either equation to find the corresponding value of x. For example, we can plug y = 6 into the equation x = -5y + 37 to find that x = -5 * 6 + 37 = -30 + 37 = <<-30+37=7>>7. Therefore, the ordered pair that is a member of both equations is (7, 6).

Answer:

77.47°

75.96°

26.57°

Step-by-step explanation:

Given vertices of the triangle:

Find the vectors from A to B, B to C and A to C:

[tex]\begin{aligned}AB = B - A &=(x_B-x_A,y_B-y_A) \\&=(-3-(-2), 8-4)\\& = (-1, 4) \end{aligned}[/tex]

[tex]\begin{aligned}BC=C-B &=(x_C-x_B,y_C-y_B)\\ &=(6-(-3),8-8)\\&=(9,0)\end{aligned}[/tex]

[tex]\begin{aligned}AC = C - A &=(x_C-x_A,y_C-x_A)\\&= (6-(-2), 8-4) \\&= (8, 4)\end{aligned}[/tex]

Use Pythagoras Theorem to calculate the magnitudes of the vectors:

[tex]|AB| = \sqrt{(-1)^2+4^2}=\sqrt{17}[/tex]

[tex]|BC|=\sqrt{9^2+0^2}=9[/tex]

[tex]|AC| = \sqrt{8^2+4^2}=4\sqrt{5}[/tex]

[tex]\boxed{\begin{minipage}{6 cm}\underline{Dot Product of two vectors}\\\\$a \cdot b=|a||b| \cos \theta$\\\\where:\\ \phantom{ww}$\bullet$ $|a|$ is the magnitude of vector a. \\ \phantom{ww}$\bullet$ $|b|$ is the magnitude of vector b. \\ \phantom{ww}$\bullet$ $\theta$ is the angle between $a$ and $b$. \\ \end{minipage}}[/tex]

Rearrange the dot product formula to make θ the subject:

[tex]\implies \theta=\cos^{-1}\left(\dfrac{a \cdot b}{|a||b|}\right)[/tex]

Use the rearranged dot product formula to find the angles between two pairs of vectors.

[tex]\boxed{\begin{minipage}{4 cm}\underline{Dot Product}\\\\$\textbf{u} \cdot \textbf{v}=u_1v_1+u_2v_2$\\\\where:\\ \phantom{ww}$\bullet$ $\textbf{u}=\left\langle u_1,u_2 \right\rangle$ \\\phantom{ww}$\bullet$ $\textbf{v}= \left\langle v_1,v_2 \right\rangle$ \\ \end{minipage}}[/tex]

Angle A

[tex]\implies A=\cos^{-1}\left(\dfrac{AB \cdot AC}{|AB||AC|}\right)[/tex]

[tex]\implies A=\cos^{-1}\left(\dfrac{-1 \cdot 8+4 \cdot4}{\sqrt{17} \cdot 4 \sqrt{5}}\right)[/tex]

[tex]\implies A=\cos^{-1}\left(\dfrac{8}{4 \sqrt{85}}\right)[/tex]

[tex]\implies A=77.47^{\circ}\; \sf (2 \; d.p.)[/tex]

Angle C

[tex]\implies C=\cos^{-1}\left(\dfrac{BC \cdot AC}{|BC||AC|}\right)[/tex]

[tex]\implies C=\cos^{-1}\left(\dfrac{9 \cdot 8+0 \cdot4}{9 \cdot 4 \sqrt{5}}\right)[/tex]

[tex]\implies C=\cos^{-1}\left(\dfrac{72}{36 \sqrt{5}}\right)[/tex]

[tex]\implies C=26.57^{\circ}\; \sf (2 \; d.p.)[/tex]

Interior angles of a triangle sum to 180°.

[tex]\implies B=180^{\circ}-A-C[/tex]

[tex]\implies B=180^{\circ}-77.47^{\circ}-26.57^{\circ}[/tex]

[tex]\implies B=75.96^{\circ}[/tex]

Therefore, the interior angles of the triangle with the given vertices are:

The standard error of X⁻, the mean from a random sample of 36 fill-ups by one driver is; 0.4167

We are given;

Mean; μ = 26 mpg

Standard deviation; σ = 2.50 mpg

Sample size; n = 36 fill ups

The formula for standard error is;

SE = Standard deviation/√Number of samples

Thus, plugging in the relevant values into the standard error formula gives;

SE = 2.5/√36

SE = 2.5/6

SE = 0.4167

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99.73 % of the points on a process control chart to fall within the UCL and LCL.

Given that,

We have to find the percentage of the points on a control chart to fall within UCL and the LCL.

We know that,

Calculating the sample data's standard deviation,. Adding three times to that sum. For the UCL, add (3 x to the average) and for the LCL, deduct (3 x from the average).

In control chart , control limits UCL and LCL are three standard deviations either side of the mean , so 99.73% of points are within the UCL and LCL.

Therefore, 99.73 % of the points on a process control chart to fall within the UCL and LCL.

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Yes, there are several ways to understand the concept of a limit in calculus without going into the details of a formal proof. One way to understand the concept of a limit is to think of it as a way to measure how close a function gets to a particular value as the input to the function gets closer and closer to a certain number. For example, if we have a function f(x) and we want to find the limit of the function as x approaches 2, we can think of this as asking "how close does f(x) get to a certain number as x gets closer and closer to 2?"

Another way to understand the concept of a limit is to think of it as a way to describe the behavior of a function as the input gets very large or very small. For example, if we have a function f(x) and we want to find the limit of the function as x approaches infinity, we can think of this as asking "how does f(x) behave as x gets very large?"

Overall, the concept of a limit is a fundamental concept in calculus that allows us to describe and analyze the behavior of functions as the input to the function changes. While a formal proof of the limit can be quite complex, there are several intuitive ways to understand the concept without going into the details of the proof.

Null hypothesis is rejected and it was concluded that proportion of the use of drugs in local seniors is more compare to national seniors.

As given in the question,

Total number of local seniors be n₁ = 100

Total number of national seniors be n₂ = 100

Let us consider proportion of local seniors be p₁

Number of local seniors using drugs = 65

Null hypothesis : p₁ = p₂

Alternative hypothesis : p₁> p₂

p₁ = 0.65

1 - p₁ = 0.35

And proportion of national seniors be p₂

Number of national seniors using drugs = 61

p₂ = 0.61

1 - p₂ = 0.39

Standard error = √ [p₁(1-p₁)/n₁ + p₂(1-p₂)/n₂]

                       = √0.65( 0.35)/100 + 0.61(0.39)/100

                       = √0.002275 + 0.002379

                       = 0.0682

Z =( p₁ - p₂ ) /  √ [p₁(1-p₁)/n₁ + p₂(1-p₂)/n₂]

  = 0.65 - 0.61 / 0.0682

  = 0.04/ 0.0682

  =0.5865

p-value = 0.2788 > 0.05

Null hypothesis rejected at the 5% level.

Therefore, from the given proportion of the distribution it is concluded that local seniors uses drugs in higher rate than the national seniors as null hypothesis rejected .

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The claim "The difference between the mean pulse rate of people who do not exercise regularly is higher than the mean pulse rate of people who exercise regularly" is true.

What is meant by mean of data?

In math, mean refers an average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers

Here we have given that a researcher was interested in comparing the resting pulse rates of people who exercise regularly and people who do not exercise regularly. Independent simple random samples were obtained of 16 people who do not exercise regularly and 12 people who do exercise regularly. The resting pulse rate (in beats per minute) of each person was recorded.

And we need to find the the claim that he difference between the mean pulse rate of people who do not exercise regularly is higher than the mean pulse rate of people who exercise regularly is true or not.

Here we have the hypothesis is H0:μ1−μ2=0H1:μ1−μ2>0

Here the Level of significance is 0.05

And the value of test statistics is calculated as,

=> t = [(X1−X2)−(μ1−μ2)]/[√S1²n1+S2²n2]

=> t = (73.5−69.3)/ [√10.2216+8.7212]

=> t = 1.1734

Hence, the value of test statistics is 1.1734.

And the critical value at 26 degree of freedom from t-table is 1.706, thus it provides insufficient evidence to reject null hypothesis.

Here, there is a direct relationship between the width of san interval or the sample standard deviation.

Therefore, if variance increases the width of an interval also increase and vice versa. Therefore, above statement is true

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The difference between the two candidate voted is less than the margin of error, so the result cannot be predicted.

4% of 2052 is 4/100 x 2052 = 82.08

44% of 2052 is 902.88

46% of 2052 is 943.92

The difference between the two candidate voted is less than the margin of error

It increases as the level of confidence increases because the larger the expected proportion of intervals that will contain the parameter the larger the margin of error.

The race was too close to call means it is within the margin of error for one candidate to receive 44% of the popular vote and for the other candidate to receive 46​%, the poll cannot predict the winner.

Therefore, The result cannot be predicted as the race was too close to call.

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Since the amounts are not provided, we have mathematically computed the correct amounts for the deductions and gross and net pay, respectively, below.

The net pay is the amount earned after allowed deductions are made to the gross pay or earnings for the period.

Some of the deductions include social security, medicare, federal income tax withholding, and retirement contributions, among others.

Total hours worked for last week = 48 hours

Hourly rate of pay = $11.00

Gross pay for the week = $528 ($11 x 48)

Social Security Tax = $32.74 (6.2% of $528)

Medicare Tax = $7.66 ($528 x 1.45%)

Federal income tax withheld = $52.80 ($528 x 10%)

401(k) Retirement savings contributions = $26.40 ($528 x 5%)

Total deductions = $119.60

Net pay for the week = $408.40 ($528 - $119.60)

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Answer:

Open circle shaded to the right

Step-by-step explanation:

Since its a more than inequality, its is shaded to the right.

Since the inequality applies to numbers GREATER than 3 you have a open circle because you are not including 3.

Answer:

just substitute each value of x into the function

Step-by-step explanation:

1. (x=-2) y= 4(-2)+2

2. (x=0) y= 4(0)+2

3. (x=2) y= 4(2)+2

4. (x=4) y= 4(4)+2

use the same steps but change the value of x. go ahead a use your calculator

The p-value for the given information is 0.247.

The p value refers to a number which is calculated from a statistical test and describes how likely a researcher is to have found a particular set of observations if the null hypothesis were true.

According to the provided information,

Sample size, n = 100

Sample proportion p’ = 47/100 = 0.47

The null hypothesis is: H0 - p = 0.5

The alternative hypothesis is: Ha - p > 0.5

Probability to be tested p = 0.5

Standard deviation = √p(1 – p)/n = √0.5(1 - 0.5)/100 = 0.05

z-test statistics is given by

z = (p’ – p)/σ = (0.47 – 0.5)/0.05 = - 0.6

From the table,

P value = 0.247

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There is only one way to represent a vertical line as an equation:

[tex]x=d[/tex]

We're given:

Both of the x-coordinates in these points are equal.

This indicates that this is a vertical line.

The x-intercept of a vertical line will always look like [tex](x,0)[/tex], where x is the same x-value as the given points.

[tex]x=3[/tex]

[tex]x=3[/tex]

Answer:

when m=3,

then,2/5×3-1/3

=6/5-1/3

=(6×3-1×5)/15

=13/15 Ans...