Name 2 lines that are perpendicular

Answer:

2/3

Step-by-step explanation:

8+6=14

14/21=2/3

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We have the function h(n) = 4x+3

h(n) = 15

4x+3 = 15

4x = 12

x= 3

And f(x) = 2(4)^x

f(3) = 2(4)³

f(3) = 2*64

f(3)= 128

The distance between the fire and station B is 10.7miles

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

The angle at A = 90- 35

= 55°

The angle at B = 90-49

= 41°

Angle at the fire = 180-(41+55)

= 180-96 = 84°

Using sine rule

sin84/13 = sin55/x

xsin84 = 13sin55

0.995x = 10.65

x = 10.65/0.995

x = 10.7 miles

Therefore the distance between the fire and station B is 10.7 miles.

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Answer: (x+6)(x-3)

Step-by-step explanation:

y=x^2+3x-18

(x+6)(x-3 )

The present value (PV) of the investment today is approximately $2,965.05.

To find the present value (PV) of the investment today, we need to calculate the present value of each individual contribution and then sum them up. We can use the formula for the present value of an annuity to do this calculation.

The formula for the present value of an annuity is given by:

PV = C * [(1 - (1 + r)^(-n)) / r]

Where:

PV = Present Value

C = Cash flow per period

r = Interest rate per period

n = Number of periods

In this case, the cash flow per period (C) is $500, the interest rate per period (r) is 10.5% (or 0.105), and the number of periods (n) is 20 years.

Let's plug in these values into the formula and calculate the present value (PV):

PV = $500 * [(1 - (1 + 0.105)^(-20)) / 0.105]

Using a calculator, we can evaluate the expression inside the brackets:

PV = $500 * [(1 - 0.376889) / 0.105]

Simplifying further:

PV = $500 * [0.623111 / 0.105]

PV = $500 * 5.930105

PV = $2,965.05

Therefore, the present value (PV) of the investment today is approximately $2,965.05.

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Using the least common factor, it is found that she will do all the three activities again on the same day again in 48 days.

To find how many days it takes so that she will do all the three activities again on the same days, we have to find the least common factor of 4, 6 and 16.

It is done factoring them using prime factors, then:

4 - 6 - 16|2

2 - 3 - 8|2

1 - 3 - 4|2

1 - 3 - 2|2

1 - 3 - 1|3

1 - 1 - 1

Hence:

lcm(4,6,8) = 2x2x2x2x3 = 48

She will do all the three activities again on the same day again in 48 days.

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i don't know how to feel about this but this is deep

bro- are you ok? like really- are you good?

False, In the exponential decay function ƒ(x) = a • bx, the b is between 0 and 1.

What is exponential decay function?

In mathematics, the term "exponential decay" refers to the process of a constant percentage rate decline in a value over time.

                     It can be written as y=a(1-b)x, where y represents the final amount, a represents the initial amount, b represents the decay factor, and x is the amount of time that has passed.

How do you calculate an exponential function?

The equation f(x) = ax, in which the input variable x appears as an exponent, describes an exponential function. Both the exponential function and the value of x are dependent on the exponential curve.

                               The exponential function, which has the form, is a significant mathematical function. f(x) = ax.

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The rule of (x, y) → (-x, y), which is reflection over y-axis.

Given that, ΔABC maps to triangle ΔA'B'C'.

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

The coordinate points of ΔABC are A(-4, 3), B(-3, -3) and C(1, 2) and the coordinate points of ΔA'B'C' are A'(4, 3), B'(3, -3) and C'(-1, 2).

Here, A(-4, 3) → A'(4, 3), x-coordinate is negated and y-coordinate remains same.

Similarly, B(-3, -3) → B'(3, -3) and C(1, 2) → C'(-1, 2) follows the same pattern.

From this, it is clear that the coordinates of triangle ABC is reflected on y-axis.

Therefore, the rule of (x, y) → (-x, y), which is reflection over y-axis.

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Answer:

\(\boxed{ \displaystyle y = 7\sin\left(\frac{2}{9}x-\frac{1}{4}\right)}\)

Step-by-step explanation:

we want to figure out the equation of a sine function that has the following characteristics.

the standard form of sine function is given by

\( \displaystyle y = a\sin(bx-c)+d\)

where:

Finding a and phase shift:

a and c is simply given which is

finding b:

using the equation we acquire:

\(\dfrac{2\pi}{b}=9\pi\)

solving the equation for b,we obtain:

b=2/9

finding d:

Since d Isn't mentioned, we would assume it 0

finding the equation:

substitute what we got:

\(\boxed{ \displaystyle y = 7\sin\left(\frac{2}{9}x-\frac{1}{4}\right)}\)

and we're done!

An equation that could be the equation of this parabola include the following: C. x = 1/12(y²).

In Mathematics, the standard equation of the directrix lines for any parabola that opens to the right is represented by this mathematical expression:

x = a(y - k)² + h.

Where:

By critically observing the graph which models the equation of this parabola, we can logically deduce that the vertex is at point (0, 0) and as such, we have the following:

h = 0

k = 0

a = positive.

x = a(y - k)² + h.

x = a(y - 0)² + 0.

x = ay²

Therefore, a possible equation is x = 1/12(y²).

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Answer:

4 large and 14 small

Step-by-step explanation:

Answer:

The answer is the 2nd one :)

Step-by-step explanation:

i got the answer right

The frosting of Molly will be a darker shade of pink.

Colors forming by combining the colors with lights is called additive color mixing. The color you get after mixing depends on the ratio of the lights you use.

For example, mixing any two colors in 1 : 1 ratio will get a different color than when you mix it in a different ratio, like 1 : 2.

In the question, it is given that Mabel and Molly are using the same amount of pink food coloring for the cake.

But Mabel is using more white buttercream frosting than Molly. So when the pink comes to mix with more white color, the resulting color becomes lighter.

This leads the cake of Mabel to be more of lighter shade which in turn make the cake of Molly to be more of darker shade.

Hence, the frosting of Molly will be a darker shade of pink.

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Step-by-step explanation:

(a) The lower limit of the 90% confidence interval can be calculated using the formula:

lower limit = sample mean - margin of error

Plugging in the given values, we have:

lower limit = 7.43 - 1.32

lower limit = 6.11 (rounded to 2 decimal places)

Therefore, the lower limit of the 90% confidence interval is approximately 6.11 hours per night.

(b) If 500 random samples like this were selected, and a 90% confidence interval was constructed using each sample, the expected number of intervals that would contain the population mean can be approximated using the margin of error as a guide.

Since the margin of error is 1.32 hours, we can expect roughly 90% of the confidence intervals to contain the true population mean. Therefore, out of 500 samples, we would expect approximately:

500 * 0.9 = 450

So, approximately 450 of these confidence intervals would contain the population mean.

Answer:

705.81 and 705.810

Step-by-step explanation:

700 + 5 + 0.8 + 0.01 = 705.81

Answers:

705.810

705.81

Answer:

3/8 or 3:8

Step-by-step explanation:

pink : not pink

6 : 16

Think of it as a fraction. Simplify it in the same way.

6/16 simplifies to 3/8

So the pink:notpink ratio is 3/8 or 3:8

Answer:

113 points per game

Step-by-step explanation:

8 basketball games

904 points in total

How many did they score per game?

______________________________

We know the Warriors scored 904 points at the end of the day, whilst having 8 basketball games said same day.

We need to split this equally to find our answer.

Divide the amount of points to the amount of games played :

904/8

113 points per game

Answer:

-16

Step-by-step explanation:

Negative four to the second power is equal to -4 x -4 which is -16

Answer:

7 boys

29 children dont own pets

there are 21 children all together

29/50

7/21

Answer:

A parallelogram is a rectangle if and only if its diagonals are congruent. A rectangle is a parallelogram with four right angles. A rhombus is a parallelogram with four congruent sides. If a parallelogram has two consecutive sides congruent, it is a rhombus.

Step-by-step explanation:

The sample's average weekly earnings have a mean of 450 according to the sampling distribution.

A continuous data distribution with a bell-shaped curve is known as a normal distribution. The mean and standard deviation of the random variable with normally distributed value is x. Moreover, a normal curve with a mean of 0 and a standard deviation of 1 is represented by the standard normal distribution. Hence, the mean and standard deviation are the variables in a normal distribution.

The median of the distribution drawn from the sample's average weekly wages is as follows:

According to the data, the sample size is 100. hence, n= 100.

The sampling distribution's mean is,

\(S_{\bar{x}} = \frac{\sigma}{\sqrt{n}}\)

    \(= \frac{50}{\sqrt{100}}\)

    = 5

Let be the sample mean. The sampling distribution of is, X is N(450,5)

This indicates that, E(X) = 450

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The correct answer is Option C. The graph represents the function f (x) = StartFraction 1 Over x EndFraction minus 1 is On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 1, and the horizontal asymptote is at y = 0.

On a coordinate plane, the graph of a hyperbola is shown.

In quadrant 1, one curve opens up and to the right, while in quadrant 3, the other curve opens down and to the left.

The vertical asymptote is at x = -1, and the horizontal asymptote is at y = 0. This hyperbola is symmetrical across both the x and y axes.

The function f(x) = 1/x - 1 has a vertical asymptote at x = 0 because the denominator approaches zero as x approaches zero.

A fraction with a denominator of zero cannot exist.

The horizontal asymptote of this function is y = -1 because as x approaches infinity or negative infinity, f(x) approaches -1.

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Answer:

43.6 has 3 significant figures.

Answer:

85

Step-by-step explanation:

it's counting by tens and the line is going in the middle of 80 and 90 so it's 85

A sample of 24 pieces of work is considered for the checking the quality of the work,

a) Upper control limit of 99.73% confidence interval is 4

Lower control limit of 99.73% confidence interval is Zero.

The process is in control because all the values of the blemishes per unit are lie within the control limits .

The Control limits consist of two limits lower control limit and upper control limit within which the value of the statistical observations of a product are expected to lie. If the values lie outside these limits, then the process is called out of statistical control. We have,

Kate Drew has been hand-painting wooden Christmas ornaments for several years.

Sample size = 24 pieces

confidence level = 99.73% = 0.9973

The number of blemishes per unit is given as:

1,1,2,3,1,0,2,0,0,1,3,1,0,1,2,0,0,2,1,2,3,2,1,1.

The control limits are to be computed for the number of defects per piece . Let us consider the number of defects per piece be denoted by c. In that case, the control limits for c chart are used. The upper control limit (UCL) and lower control limit (LCL) for c chart is given by,

UCL = c-bar + 3 s.d

LCL = c-bar - 3 s.d

where c-bar = 1/n(€c) average number of defects

So, c-bar is computed as,

c-bar = (1+1+2+3+1+0+2+0+0+1+3+1+0+ 1+2+0 +0+2 + 1+2 +3+ 2+1+1) /24 = 30/24 = 1.25

put the data in Excel sheet and calculate required limits using Excel Commands.

Excel Command for Average, c-bar

=Average( Range of numbers who's average you want to calculate )

In my excel sheet, = Average ( H2 : H25)

= 1.25

Excel Command for Standard deviations,

=STDEV( numbers who's standard deviations you want to calculate)

here, =STD(H2:H25) , output= 0.98907

UCL = 1.25 + 3( 0.98907)

= 4.217

LCL = 1.25 - 3( 0.98907)

= - 1.717

but defective item can never be negative so, Lower control limit is Zero.

Hence, for the given data, the upper control limit for the number of defects is 4 and the lower control limit is 0.

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Answer:

189.84%

Step-by-step explanation:

We make the say that 64 is 100% because it is our output value.

Next up we represent the value we seek with $x$.

Therefore it follows us up with $100\%=64$.

That also gives us the same vein, $x\%=121.5$.

Which then gives you and I a pair of simple equations: 100\%=64(1) and x\%=121.5

Then by dividing the equation 1 by equation 2 and taking note of the faction of both equations. They then have the same unit (%); we got.

Then you just keep doing what you learned and eventually you will get $121.5$ is $189.84375\%$ of $64$.

Therefore, $121.5$ is $189.84375\%$ of $64$.

Given that a ∇ b = 4, it doesn't matter what values you choose for a and b, the result of the ∇ operation is always 4.

So, unless your question is missing some additional details, we have

(4 ∇ 3) ∇ 6 = 4 ∇ 6 = 4

and

(7 ∇ 2) ∇ 5 = 4 ∇ 5 = 4

Answer:

0

Step-by-step explanation:

4r-10s

4x5-10x2

20-20

= 0

Answer:

about 100 feet

Step-by-step explanation:

Answer:

Step-by-step explanation:

To write y as a function of x using the given functions, we can substitute the value of "a" in the first equation with the expression "-5x + 1" from the second equation.

Given:

y = -3a + 3

a = -5x + 1

Substituting the value of "a" in the first equation:

y = -3(-5x + 1) + 3

Now, let's simplify this expression:

y = 15x - 3 + 3

y = 15x

Therefore, y can be expressed as a function of x as:

y = 15x