line Q passes through points (3,9) and ( 10,5) line R is perpendicular to Q what is the slope of
line R

Probability of distinct 3-digits is 1/6.

Probability of both the first digit and the last digit are even numbers is 1/5.

Step-by-step explanation:

Given set of numbers {1,2,3,5,8,9} = 6

Total number of 3-digits can be formed = 6[tex]\times[/tex]5[tex]\times[/tex]4 = 120.

Probability  of the three-digit numbers with distinct digits :

The number of 3-digit numbers with distinct digits = (6[tex]\times[/tex]5[tex]\times[/tex]4) / (3[tex]\times[/tex]2[tex]\times[/tex]1) = 20.

P(distinct 3-digits) =  no. of distinct 3-digits / Total no.of 3-digits

⇒ 20/120

⇒ 1/6

Probability that both the first digit and the last digit of the three-digit number are even numbers :

The even numbers in the set are 2 and 8 = 2 possibilities.

The number of 3-digits with 1st and 3rd digit are even = (2[tex]\times[/tex]6[tex]\times[/tex]2) = 24.

P(1st and 3rd digits even)= no. of 1st and 3rd digit even/Total no. of 3-digits.

⇒ 24/120

⇒ 1/5

Answer:

C

Step-by-step explanation:

Subtraction Property

10x - 30 = 7x

Subtract 7x from both sides.

3x - 30 = 0

Answer: k = -17

Step-by-step explanation:

K -7= -24

k= -24 + 7

k = -17

Answer:

the height is 3

the with is also 3 because

1.5+1.5=3

The equation [tex]y=2x+2[/tex] is a function

Explanation:

Given that the graph contains the coordinates [tex](-1,0)[/tex], [tex](0,2)[/tex] , [tex](1,4)[/tex] and [tex](2,6)[/tex]

We need to determine whether the equation [tex]y=2x+2[/tex] is a function.

To determine the equation is a function, let us substitute the coordinates in the equation and check whether it satisfies the equation.

Let us substitute the coordinate [tex](-1,0)[/tex] in the equation [tex]y=2x+2[/tex]

Thus, we have,

[tex]0=2(-1)+2[/tex]

[tex]0=-2+2[/tex]

[tex]0=0[/tex]

Thus, the coordinate [tex](-1,0)[/tex] satisfies the equation [tex]y=2x+2[/tex]

Substituting the coordinate [tex](0,2)[/tex] in the equation, we have,

[tex]2=2(0)+2[/tex]

[tex]2=2[/tex]

Thus, the coordinate [tex](0,2)[/tex] satisfies the equation [tex]y=2x+2[/tex]

Substituting the coordinate [tex](1,4)[/tex] in the equation [tex]y=2x+2[/tex]

[tex]4=2(1)+2[/tex]

[tex]4=4[/tex]

Thus, the coordinate [tex](1,4)[/tex] satisfies the equation [tex]y=2x+2[/tex]

Substituting the coordinate [tex](2,6)[/tex] in the equation, we get,

[tex]6=2(2)+2[/tex]

[tex]6=6[/tex]

Thus, the coordinate [tex](2,6)[/tex] satisfies the equation [tex]y=2x+2[/tex]

Hence, the coordinates [tex](-1,0)[/tex], [tex](0,2)[/tex] , [tex](1,4)[/tex] and [tex](2,6)[/tex] satisfies the equation [tex]y=2x+2[/tex]

Thus, the equation [tex]y=2x+2[/tex] is a function.

Answer:

Part A - 4x + 8 dollars

Part B - $45

Step-by-step explanation:

The account balance will be $6642 after seven years.

Step-by-step explanation:

To find the amount after seven years, a certain formula is used.

Amount = [tex]P( 1+r/n)^{n\times t}[/tex]

where,

P is the principal amount that is invested in the account.

Therefore, P = 4500 dollars.

r is the rate of interest. (r = 5.5 %)

Therefore, r = 5.5/100 = 0.055

n is the number of time the interest is compounded per year which is n= 4.

t is the time period which is t = 7 years.

Now, substituting all the above values in the formula,

Amount = [tex]4500(1+0.055/4)^{4\times 7}[/tex]

⇒ [tex]4500(4.055/4)^{28}[/tex]

⇒ [tex]4500(1.014)^{28}[/tex]

⇒ [tex]4500\times1.4759[/tex]

⇒ 6641.55 (which is approximately equal to 6642)

⇒ 6642 dollars.

The account balance after 7 years is $6642.

Answer:

4

Step-by-step explanation:

we add them then divide 2

(11/2+2 1/2)/2

To construct a histogram, you must decide on your interval size by dividing the data range by your desired number of intervals. Then, sketch the graph with scaled axes and intervals consistently to accurately represent the data.

To construct a histogram, you need to determine the interval size for your bins. The interval size depends on the range of your data and the number of intervals you want to use. For instance, if you have data ranging from 32.5 to 100.5 and you want to create five intervals, you subtract the smallest value from the largest and then divide by the number of intervals. So it would be (100.5 - 32.5) ÷ 5, which equals 13.6. This means each interval would be 13.6 units wide.

When constructing the actual histogram, the x-axis would cover from 32.5 to 100.5 and the y-axis would cover the frequency of the data within each interval. An interval's endpoints can be determined successively by adding the interval width to the previous endpoint, starting with 32.5. Moreover, for data with a small range like 1 to 6, you could create six intervals ranging from 0.5 to 6.5 to ensure all data points are included, with a 1 unit interval size for clarity.

Sketch the graph using a ruler and pencil, and carefully scale the axes to accurately reflect the range and intervals for the data you're representing. Consistency in interval size is key when placing data values into each bin.

Final answer:

A histogram is constructed by determining the number of intervals, with a common range being five to 15 intervals. Calculate the interval width by dividing the total range of data by the chosen number of bins. Use a ruler and pencil for a scaled and precise histogram representation.

Explanation:

To construct a histogram, you need to decide on the number of intervals, also known as classes or bins. In this case, the data provided suggests we need to create five to six intervals. The x-axis for our histogram might range from 32.5 to 100.5, representing the data values, and the y-axis records the frequency of the data points.

To calculate the width of each interval, take the range of the data (100.5 - 32.5 = 68) and divide it by the number of intervals (5). This gives us an interval width of 13.6. When scaling the axes, use a ruler and pencil for precision.

For example, if your data set ranges from a smallest value of 1 to a largest value of 6, you might set your bins to start at 0.5 and end at 6.5 to ensure that all values are included. With this range of 6 (6.5 - 0.5), and deciding on six bins, the bin size or interval size would be 1. This is explained in Solution 2.10.

Remember to consistently apply the same method when placing data values within intervals to enable comparability and clarity in your histogram.

The chances of winning the grand prize in this game are approximately 0.089, whereas the chances of winning the consolation prize are 0.01.

The subject of this question is Probability, which is a branch of Mathematics. To calculate the probability, we'll need to determine the total number of outcomes and the count of the favorable outcomes.

a) To win the grand prize, all three balloons popped have to have 'Winner' slips. The probability of each dart hitting such a balloon will decrease as the total number of balloons decreases. First dart probability would be 5/8 (5 'Winner' balloons out of 8 total), the second one 4/7 (as one 'Winner' balloon is already popped), and 3/6 for the third. Multiply these probabilities together to get the overall probability: (5/8) * (4/7) * (3/6) = 0.089 (rounded to the third digit).

b) Similarly, for the consolation prize, we would have to hit all three balloons with blank slips. The process is equivalent, resulting in a probability of (3/8) * (2/7) * (1/6) = 0.01 (rounded to the third digit).

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Step-by-step explanation:

Look at the picture.

Hmm.... If the angle θ is correctly marked on your photo, then your solution is incorrect.

You write the function values ​​but for the angle 180° - θ.

[tex]\sin(180^o-\theta)=\sin\theta\\\cos(180^o-\theta)=-\cos\theta\\\tan(180^o-\theta)=-\tan\theta\\\cot(180^o-\theta)=-\cot\theta[/tex]

Therefore

for

[tex]x=-7,\ y=24,\ r=\sqrt{(-7)^2+24^2}=\sqrt{49+576}=\sqrt{625}=25[/tex]

Let θ be this angle in your picture.

[tex]\sin\theta=\dfrac{24}{25}\\\\\cos\theta=-\dfrac{-7}{25}=\dfrac{7}{25}\\\\\tan\theta=-\dfrac{24}{-7}=\dfrac{24}{7}\\\\\cot\theta=-\dfrac{-7}{24}=\dfrac{7}{24}\\\\\sec\theta=\dfrac{1}{\cos\theta}=\dfrac{1}{\frac{7}{25}}=\dfrac{25}{7}\\\\\csc\theta=\dfrac{1}{\sin\theta}=\dfrac{1}{\frac{24}{25}}=\dfrac{25}{24}[/tex]

Expressions a, b, and d are equivalent to 5^3. They all follow the laws of exponents, resulting in the same value of 5^3, or 125.

The question is asking which expressions are equivalent to 5^3. Let's break down each option:

So, options a, b, and d are equivalent to 5^3.

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(12, 11):

2((12) + 3) - (11) = 7 + (12)

2 • 15 - 11 = 19

2 • 4 = 19

8  [tex]\neq[/tex]  19

(1, 0):

2((1) + 3) - (0) = 7 + (1)

2 • 4 = 8

8 = 8

(-5, 1):

2((-5) + 3) - (1) = 7 + (-5)

2 • -2 - 1 = 2

2 • -3 = 2

-6  [tex]\neq[/tex]  2

Hope this helps.

Answer:

1 pencil = $0.75

1 eraser = $0.29

Step-by-step explanation:

4p+2e=3.58                                 1p+6(0.29)=2.49

1p+6e=2.49                                   1p+1.74=2.49

p=2.49-6e                                     1p=0.75

4(2.49-6e)+2e=3.58                       p=0.75

9.96-24e+2e=3.58

9.96-22e=3.58

-22e=-6.38

e=0.29

Answer:

Step-by-step explanation:

Let w be the width

Length = 3w +15

Perimeter = 94 cm

2*(length + width) = 94

2*(3w+15 + w) = 94

2*( 4w + 15) = 94

4w + 15 = 94/2

4w +15 = 47

        4w = 47 -15

         4w = 32

           w = 32/4

          w = 8 cm

Length = 3w +15 = 3*8 + 15 = 24 +15 = 39

Length = 39cm

Area = length * width = 39*8 = 312

Area = 312 cm²

The area of the rectangle is [tex]\( \boxe{312 \, \text{cm}^2} \).[/tex]

Step 1

Let's denote the width of the rectangle as w cm.

According to the problem, the length of the rectangle is [tex]\( 15 \)[/tex] cm more than three times its width. So, the length [tex]\( l \)[/tex] can be expressed as [tex]\( 3w + 15 \)[/tex]cm.

The perimeter P of a rectangle is given by:

[tex]\[ P = 2(l + w) \][/tex]

Given that the perimeter of the rectangle is [tex]\( 94 \)[/tex] cm, we can write the equation:

[tex]\[ 94 = 2((3w + 15) + w) \][/tex]

Step 2

Now, let's solve for [tex]\( w \)[/tex]:

[tex]\[ 94 = 2(4w + 15) \]\[ 94 = 8w + 30 \]\[ 8w = 94 - 30 \]\[ 8w = 64 \]\[ w = \frac{64}{8} \]\[ w = 8 \][/tex]

Step 3

Now that we have found the width of the rectangle to be [tex]\( 8 \)[/tex] cm, we can find its length:

[tex]\[ l = 3w + 15 \]\[ l = 3(8) + 15 \]\[ l = 24 + 15 \]\[ l = 39 \][/tex]

Step 4

Now that we have the width [tex]\( w = 8 \)[/tex] cm and the length [tex]\( l = 39 \)[/tex] cm, we can calculate the area A of the rectangle:

[tex]\[ A = l \times w \]\[ A = 39 \times 8 \]\[ A = 312 \][/tex]

So, the area of the rectangle is [tex]\( \boxe{312 \, \text{cm}^2} \).[/tex]

Circumference of the circle = 94.2 yd

Solution:

Given data:

Diameter of the circle = 30 yd

The value of π = 3.14

To find the circumference of the circle:

Circumference of the circle = πd

Substitute the diameter value in the formula, we get

Circumference of the circle = 3.14 × 30

                                              = 94.2

Circumference of the circle = 94.2 yd

Answer:

6

Step-by-step explanation:

10^3 = 1000

1000 x 0.006 = 6

Answer: 373/50

Step-by-step explanation:

Step 1: convert to a fraction

746% = 746 ÷ 100 = 7.46

7.46 = 373/50

Step 2: Write the number as a fraction of one: 7.46 = 746/100

Step 3: use a common divisor of 2 to reduce the numbers, we have

(746÷2)= 373

(100÷2)=50

when reduced to the simplest form= 373/50

Therefore, 746/ 100 = 373/50 when expressed as a mixed number.

Answer: 373/50

Step-by-step explanation:

Step 1) Since 746% is a percent, it is written over the denominator of 100. So first convert it to a fraction, which would be 746/100.

Step 2) Find the GCF (greatest common factor). In order to find the GCF start by writing all the factors of

100:

1, 2, 4, 5, 10, 20, 25, 50, 100

Step 3) Now test every number there and see if any go into 746. Start at the highest number, which in this case is 100. (Example, ask yourself, “does 100 go into 746? No.” Then try with 50, and continue until you get to a number that goes into 746 evenly.)

Step 4) The GCF from the previous step is 2. So now divide 746 by 2 (answer is 373) and 100 by 2 (answer is 50).

Step 5) Now put 373/50 and that’s your answer! Congratulations you finished it!

Answer:

87.92 in²

Step-by-step explanation:

pi × (R² - r²) = area

Where R is the radius of the outer circle and r of the inner circle.

Since C = 2pi×r

37.68 = 2×3.14×r

r = 6 in

R = 6 + 2 = 8 in

Therefore,

pi × (R² - r²) = area

Area = 3.14 (8² - 6²)

= 87.92 in²

Answer:

The ratio is the same as the ratio of the angle of that sector to the angle for the whole circle (2π).

Step-by-step explanation:

Answer:

4,212

Step-by-step explanation:

Step 1:  Add

23 + 4189

4,212

Answer:  4,212

Answer:

Step-by-step explanation:

a) (5,5) ;    (10,6);  slope = 1/5

  (x1,y2);    (x2,y2)

y-y1 = m (x-x1)

[tex]y-5=\frac{1}{5}*(x-5)\\\\y-5=\frac{1}{5}*x-\frac{1}{5}*5\\\\y-5=\frac{1}{5}x-1\\y=\frac{1}{5}x-1+5\\\\y=\frac{1}{5}x+4[/tex]

d) (√2,7)    ; (√2,-7)

  (x1,y1)    ; (x2,y2)

[tex]slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{-7-7}{\sqrt{2}-\sqrt{2}}\\\\=\frac{-14}{0}=0[/tex]

Equation: y =7 or y = -7

Answer:

4x - 12

Step-by-step explanation:

Distribute the 4 to the x and -3.

4 × x = 4x

4 × -3 = -12

4x - 12

Answer:

452.39 feet³

Step-by-step explanation:

In the attached file

Answer:

452.4

Step-by-step explanation

π·r²·h

π·3²·16

π·9·16

π·144

452.38

round that up to the tenths place it's 452.4

Answer:

The answer should be 45

Step-by-step explanation:

To get the whole are you would have to multiply the lenght with the Width and then take that answer and multiply it with the height

BUT

because you want the surface area, it would be just the lenght and width

15x3=45

so 45 is your answer.

Initial equation:

4a / 2 = 5.2

Multiply both sides by 2:

4a = 10.4

Divide both sides by 4:

a = 2.6

Hope this helps!! :)

Answer:

Step-by-step explanation:

2.6 becuase 4a/2= 5.2

4a=10.4

a=2.6

Answer: 0.00108154877

Step-by-step explanation:

The division [tex]\frac{5}{4623}[/tex] results in the simple decimal 0.001081603. This expression is already reduced to the most basic fraction form of itself.

The division is an arithmetic operation that involves splitting a quantity or number into equal parts or groups. It is the inverse operation of multiplication. In division, a number called the dividend is divided by another number called the divisor to obtain the quotient.

The dividend is the total quantity or number being divided, while the divisor is the number by which the dividend is divided. The result of the division is called the quotient, which represents the number of times the divisor can be subtracted from the dividend to achieve equal parts.

Given the expression [tex]\frac{5}{4623}[/tex] ,

[tex]\frac{5}{4623}[/tex] = 5 [tex]\div[/tex] 4623 = 0.001081603.

Learn more about Division here:

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The slope represents the rate of change. Then the rate of change will be 4.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given below.

y = 4x + 60

The slope is 4 and the y-intercept is 60.

The slope represents the rate of change. Then the rate of change will be 4.

More about the linear equation link is given below.

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The rate of change in the equation y = 4x + 60 is 4, which is the coefficient of x. This means for each unit increase in 'x', 'y' will increase by 4 units.

In mathematics, the rate of change in an equation like y = 4x + 60 is represented by the coefficient of the variable x. This is because, in such an equation which is in the form of y = mx + b (a standard linear equation), 'm' represents the rate of change or the slope of the line.

So, in your specific equation y = 4x + 60, the rate of change or slope is 4. This means that for each increment of 1 in 'x', 'y' will increase by 4 units. This value - 4 - is your rate of change in this case.

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