Determine the area under the standard normal curve that lies between (a) Z = - 1.46 and Z=146, (b) Z-168 and 2-0, and (c) Z= -1.34 and Ze-0.31 GOGO (a) The area that lies between Z=- 146 and 2.146 is (Round to four decimal places as needed.) (b) The area that lies between Z=-168 and 2018 | (Round to four decimal places as needed) (c) The area that lies between Z= -134 and Z=-0.311 (Round to four decimal places as needed)

Answer:

Step-by-step explanation:

17

Answer:

Step-by-step explanation:

A quadrilateral with perpendicular diagonals, one of which is a line of symmetry, is a kite.

Perhaps a more conventional definition of a kite is that it is a quadrilateral with two pairs of congruent adjacent sides.

The lengths PS and SR can be found by counting grid squares along the line segments. Each has a length of 3. They constitute one pair of congruent adjacent sides.

  PS = SR = 3

__

The lengths of PQ an QR can be found using the distance formula. Essentially, it uses the Pythagorean theorem to compute the hypotenuse of a right triangle whose legs are the differences in x- and y-coordinates. For PQ and QR, those differences are 2 and 5, so the lengths of those segments are √(2² +5²) = √29.

  PQ = QR = √29

__

The figure has two pairs of congruent adjacent sides, so is a kite.

The total charge for the month is £625.36.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given:

Fixed monthly plan - 616

free minutes - 150

Used minutes - 170

Free text - 150

Used text - 182

Charging amount over the free limit - 18p

Number of minutes over the limit -  170 - 150 = 20

Number of text over the limit - 182 - 150 = 32

So the extra amount that will be added to the monthly charge would be -

(20 x 0.18) +(32 x 0.18)

The total charge of the month would be -

C= 616+(20*0.18) +(32*0.18)

C= 616+3.60+5.76

C= 625.36

Therefore, the total charge for the month is £625.36.

The correct question is given below,

Here are the monthly charges for Jo's mobile phone

Monthly charge 616

150 free minutes, then 18p per minute

150 free texts, then 18p per text

During one month, Jo makes 170 minutes of calls and sends 182 texts,

Work out the total charge for the month

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The scatterplot with the least squares line provides insights into the relationship between average annual global surface temperature and the years from 2000 to 2015, allowing us to assess trends, strength of correlation, and make predictions within certain limitations.

The scatterplot represents the relationship between the average annual global surface temperature, in degrees Celsius, and the corresponding years from 2000 to 2015. The line drawn on the plot is the least squares line, which is the best fit line that minimizes the overall distance between the observed data points and the line.

The least squares line is determined using a statistical method called linear regression. It calculates the equation of a straight line that represents the trend in the data. This line serves as a mathematical model to estimate the average temperature based on the year.

By analyzing the scatterplot and the least squares line, we can make several observations. Firstly, we can see whether the temperature has been increasing, decreasing, or remaining relatively stable over the given years. If the slope of the line is positive, it indicates a positive correlation, implying that the temperature has been increasing. Conversely, a negative slope suggests a decreasing trend.

Additionally, we can evaluate the strength of the relationship between temperature and time by examining how closely the data points cluster around the line. If the points are closely grouped around the line, it suggests a strong correlation, indicating that the line is a good representation of the data. On the other hand, if the points are more scattered, the correlation may be weaker.

Furthermore, the line can be used to predict the average annual global surface temperature for future years beyond the data range of 2000 to 2015. However, it's important to note that such predictions should be made with caution and considering other factors that may affect global temperatures, such as climate change and natural variability.

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Question

The given scatterplot shows the average annual global surface temperature, in degrees celsius, for each year from 2000 to 2015. the line drawn is the least squares line for the data set.

3. EFG and GFI, EFH and HFI are supplementary. EFG and GFI are complementary.

4. A = 25, B = 65

5. m∠BAE = 80

m∠QRP = 100

Let us solve each question one by one-

3. We know that the angles on a straight line are supplementary. Thus, two pairs of supplementary angles are-

EFG + GFI = 180

EFH + HFI = 180

It is also given that GFI is 90

and as EFG + GFI = 180

EFG = 90

Thus, EFG and GFI are a pair of complementary angles.

4. Let the measure of angle A = x

then, the measure of angle B = 2x + 15

As these two angles are complementary-

x + 2x + 15 = 90

3x + 15 = 90

3x = 75

x = 25

Thus angle A = 25

and angle B = 2(25) + 15 = 65

5. m∠BAE = 3x + 5

m∠QRP = 5x - 25

As these two angles are supplementary-

m∠BAE + m∠QRP = 180

3x + 5 + 5x - 25 = 180

8x - 20 = 180

x = 200/8

x = 25

Thus, m∠BAE = 3(25) + 5 = 80

m∠QRP = 5(25) - 25 = 100

6. Callista's statement is true.

For example if there are 2 pairs of supplementary angles-

m∠A + m∠B = 180

and m∠B + m∠C = 180

m∠B = 180 - m∠C

m∠A + 180 - m∠C = 180

m∠A - m∠C = 0

m∠A = m∠C

Thus, we've proved that if 2 angles are supplementary to the same angle, they must be equal.

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Answer:

OP = discount amount × 100 / discount %

Step-by-step explanation:

if I understand this correctly, the actual sale price was 36% (100-64) of the originally marked price.

original price (OP) = 100%

64% of OP = 30

1% of OP = 30/64

OP (100%) = 100 × 30/64

this could be simplified to 100 × 15/32, but this hinders is finding the global formula :

OP = discount amount × 100 / discount %

Answer:

true

Step-by-step explanation:

so lets start with inserting some number in place of the letters

( 1 +2 ) + 3 = 1 + ( 2 + 3 )

3 + 3 = 1 + 5

6 = 6

so both side are equal that's means the equation is true

The Fundamental Pythagorean Identity in trigonomety sin²(x)+cos²(x)=1

Using  the Pythagorean Identity: \(\frac{1-2cos^2x}{sinxcosx}=tanx-cotx\) ,

Hence prove.

Trigonometry formulas can be used to address many different kinds of issues. These issues could involve Pythagorean identities, product identities, trigonometric ratios (sin, cos, tan, sec, cosec, and cot), etc. Many formulas, such as those involving co-function identities (shifting angles), sum and difference identities, double angle identities, half-angle identities, etc., as well as the sign of ratios in various quadrants,

We know that the Pythagorean theorem,

sin²(x)+cos²(x)=1

We have

1-2cos²x = sin²(x)+cos²(x) -2cos²x

1-2cos²x = sin²(x)-cos²(x)

\(\frac{1-2cos^2x}{sinxcosx}=tanx-cotx\)

To prove this take the right-hand sides

\(\frac{sin^2x}{sinxcosx}-\frac{cos^2x}{sinxcosx}\\\\=\frac{sinx}{cosx}-\frac{cosx}{sinx}\\\\= tanx-cotx\)

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Answer:

2

Step-by-step explanation:

Lines that are parallel have the same slope, so all lines parallel to the one given have the same slope as it does.  That slope value is most easily seen by transforming the given equation to slope-intercept form

(y = mx + b).

This line would be y = 2x -7, so the slope of any line parallel to it must have a slope value of 2

9514 1404 393

Answer:

Step-by-step explanation:

The end result after the final transformation is ...

  (x, y) ⇒ (-x, y)

so, each x-coordinate is negated. The transformed coordinates are ...

  S(-5, -3) ⇒ S''(5, -3)

  T(-1, 0) ⇒ T''(1, 0)

  U(-4, 1) ⇒ U''(4, 1)

  V(-4, 0) ⇒ V''(4, 0)

The maximum possible error that will be associated with the estimate when the analyst uses a sample size of 400 observations is 3.78 percent and the sample size that the analyst would need in order to have the maximum error be no more than ±5 percent is 297 observations.

The maximum possible error that will be associated with the estimate when the analyst uses a sample size of 400 observations is 3.78 percent.

Error formula for proportion:

Maximum possible error = z * √(p^ * (1-p^)/n)

Where z = 1.65 for 90 percent confidencep^

              = 0.3n

              = 400

Substitute the given values into the formula:

Maximum possible error = 1.65 * √(0.3 * (1-0.3)/400)

Maximum possible error = 1.65 * √(0.3 * 0.7/400)

Maximum possible error = 1.65 * √0.0021

Maximum possible error = 1.65 * 0.0458

Maximum possible error = 0.0756 or 7.56% (rounded to two decimal places)

b. The sample size that the analyst would need in order to have the maximum error be no more than ±5 percent can be calculated as follows:

Error formula for proportion:

Maximum possible error = z * √(p^ * (1-p^)/n)

Where z = 1.65 for 90 percent confidencep^ = 0.3n = ?

Maximum possible error = 0.05

Substitute the given values into the formula:

0.05 = 1.65 * √(0.3 * (1-0.3)/n)0.05/1.65

        = √(0.3 * (1-0.3)/n)0.0303

        = 0.3 * (1-0.3)/nn

        = 0.3 * (1-0.3)/(0.0303)n

        = 296.95 or 297 (rounded up to the nearest whole number)

Therefore, the sample size that the analyst would need in order to have the maximum error be no more than ±5 percent is 297 observations.

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In the given formula we have variables:

If we have to solve it for P then it should be called 'Principal' or 'Loan amount'.

If we have to solve it for n then it should be called 'Number of payments' or 'Number of installments'.

Since n is the power of a number we need logarithm to solve it for n.

Answer:

"Principal (loan amount)"

"Term of the loan (in months)" or "Number of monthly payments"

Logarithms

Step-by-step explanation:

Monthly Payment Formula

\(M=\dfrac{Pr\left(1+r\right)^n}{\left(1+r\right)^n-1}\)

where:

If we solve for P, the name of the formula is "Principal (loan amount)".

If we solve for n, the name of the formula is "Term of the loan (in months)" or "Number of monthly payments".

When solving for n, we need to use logarithms:

\(\boxed{\begin{aligned}M&=\frac{Pr\left(1+r\right)^n}{\left(1+r\right)^n-1}\\\\M(\left(1+r\right)^n-1)&=Pr\left(1+r\right)^n\\\\\frac{\left(1+r\right)^n-1}{\left(1+r\right)^n}&=\frac{Pr}{M}\\\\1-\frac{1}{\left(r+1\right)^n}&=\frac{Pr}{M}\\\\\frac{1}{\left(r+1\right)^n}&=1-\frac{Pr}{M}\\\\\left(r+1\right)^{-n}&=1-\frac{Pr}{M}\\\\\ln \left(r+1\right)^{-n}&=\ln \left(1-\frac{Pr}{M}\right)\\\\-n\ln(r+1)&=\ln\left(1-\frac{Pr}{M}\right)\\\\n&=\frac{-\ln\left(1-\frac{Pr}{M}\right)}{\ln(r+1)}\end{aligned}}\)

Step-by-step explanation:

The equation that represents how much will be in the account after 7 years is:

M = 7,600(1+0.06)^7

Here's the explanation:

The formula for calculating the future value (M) of a present value (P) invested at an annual interest rate (r) for a certain number of years (t) is M = P(1+r)^t.

In this case, the present value (P) is 7,600 dollars, the annual interest rate (r) is 6% or 0.06, and the number of years (t) is 7.

Substituting these values into the formula, we get M = 7,600(1+0.06)^7. This represents how much will be in the account after 7 years if no money is added or removed from the account.

The coordinate of point x is 12

The number line that completes the question is added as an attachment

The ratio is given as:

mx :xj = 3:1.

Also, we have:

M = 2

J = 18

So, we have

x = mx/(mx + xj) * (J - M)

This gives

x = 3/4 * (18 - 2)

Evaluate

x = 12

Hence, the coordinate of point x is 12

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The equation of the hyperbola centered at (-2, -4) with vertices at (-3, -4) and (-1, -4) and foci 10 units apart is ((x+2)^2)/(1/4) - ((y+4)^2)/(124/4) = 1, or equivalently, (x+2)^2/0.25 - (y+4)^2/31 = 1.

The center of the hyperbola is the midpoint of the segment between the vertices, which is ((-3-1)/2, (-4-4)/2) = (-2, -4). Since the foci are 10 units apart, the distance from the center to each focus is c = 10/2 = 5. The distance between the vertices is 2a, where a is the distance from the center to each vertex, so a = |-3 - (-2)|/2 = 1/2. The distance between each focus and vertex is b, where b^2 = c^2 - a^2, so b = sqrt(5^2 - (1/2)^2) = sqrt(124)/2. The equation of the hyperbola centered at (-2, -4) with vertices at (-3, -4) and (-1, -4) and foci 10 units apart is ((x+2)^2)/(1/4) - ((y+4)^2)/(124/4) = 1, or equivalently, (x+2)^2/0.25 - (y+4)^2/31 = 1.

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Answer: John walks a total of 360 yards from school.

Step-by-step explanation:

Let's represent the total distance John walks from school as "x".

According to the problem, John has already walked 15% of the way, which can be written as:

0.15x

We also know that he has walked 54 yards so far, which means:

0.15x = 54

To find the total distance John walks from school, we can solve for "x" by dividing both sides of the equation by 0.15:

x = 54 ÷ 0.15

x = 360

Therefore, John walks a total of 360 yards from school.

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Answer:

A

Step-by-step explanation:

Find the vertex form of the quadratic function below.

y = x^2 - 4x + 3

This quadratic equation is in the form y = a{x^2} + bx + cy=ax  

2

+bx+c. However, I need to rewrite it using some algebraic steps in order to make it look like this…

y = a(x - h)^2 + k

This is the vertex form of the quadratic function where \left( {h,k} \right)(h,k) is the vertex or the “center” of the quadratic function or the parabola.

Before I start, I realize that a = 1a=1. Therefore, I can immediately apply the “completing the square” steps.

STEP 1: Identify the coefficient of the linear term of the quadratic function. That is the number attached to the xx-term.

STEP 2: I will take that number, divide it by 22 and square it (or raise to the power 22).

STEP 3: The output in step #2 will be added and subtracted on the same side of the equation to keep it balanced.

Think About It: If I add 44 on the right side of the equation, then I am technically changing the original meaning of the equation. So to keep it unchanged, I must subtract the same value that I added on the same side of the equation.

STEP 4: Now, express the trinomial inside the parenthesis as a square of a binomial, and simplify the outside constants.

After simplifying, it is now in the vertex form y = a{\left( {x - h} \right)^2} + ky=a(x−h)  

2

+k where the vertex \left( {h,k} \right)(h,k) is \left( {2, - 1} \right)(2,−1).

Visually, the graph of this quadratic function is a parabola with a minimum at the point \left( {2, - 1} \right)(2,−1). Since the value of “aa” is positive, a = 1a=1, then the parabola opens in upward direction.

Example 2: Find the vertex form of the quadratic function below.

The approach to this problem is slightly different because the value of “aa” does not equal to 11, a \ne 1a  



​  

=1. The first step is to factor out the coefficient 22 between the terms with xx-variables only.

STEP 1: Factor out 22 only to the terms with variable xx.

STEP 2: Identify the coefficient of the xx-term or linear term.

STEP 3: Take that number, divide it by 22, and square.

STEP 4: Now, I will take the output {9 \over 4}  

4

9

​  

 and add it inside the parenthesis.

By adding {9 \over 4}  

4

9

​  

 inside the parenthesis, I am actually adding 2\left( {{9 \over 4}} \right) = {9 \over 2}2(  

4

9

​  

)=  

2

9

​  

 to the entire equation.

Why multiply by 22 to get the “true” value added to the entire equation? Remember, I factored out 22 in the beginning. So for us to find the real value added to the entire equation, we need to multiply the number added inside the parenthesis by the number that was factored out.

STEP 5: Since I added {9 \over 2}  

2

9

​  

 to the equation, then I should subtract the entire equation by {9 \over 2}  

2

9

​  

 also to compensate for it.

STEP 6: Finally, express the trinomial inside the parenthesis as the square of binomial and then simplify the outside constants. Be careful combining the fractions.

It is now in the vertex form y = a{\left( {x - h} \right)^2} + ky=a(x−h)  

2

+k where the vertex \left( {h,k} \right)(h,k) is \left( {{{ - \,3} \over 2},{{ - 11} \over 2}} \right)(  

2

−3

​  

,  

2

−11

​  

).

Example 3: Find the vertex form of the quadratic function below.

Solution:

Factor out - \,3−3 among the xx-terms.

The coefficient of the linear term inside the parenthesis is - \,1−1. Divide it by 22 and square it. Add that value inside the parenthesis. Now, figure out how to make the original equation the same. Since we added {1 \over 4}  

4

1

​  

 inside the parenthesis and we factored out - \,3−3 in the beginning, that means - \,3\left( {{1 \over 4}} \right) = {{ - \,3} \over 4}−3(  

4

1

​  

)=  

4

−3

​  

 is the value that we subtracted from the entire equation. To compensate, we must add {3 \over 4}  

4

3

​  

 outside the parenthesis.

Therefore, the vertex \left( {h,k} \right)(h,k) is \left( {{1 \over 2},{{11} \over 4}} \right)(  

2

1

​  

,  

4

11

​  

).

Example 4: Find the vertex form of the quadratic function below.

y = 5x^2 + 15x - 5  

Solution:

Factor out 55 among the xx-terms. Identify the coefficient of the linear term inside the parenthesis which is 33. Divide it by 22 and square to get {9 \over 4}  

4

9

​  

.

Add {9 \over 4}  

4

9

​  

 inside the parenthesis. Since we factored out 55 in the first step, that means 5\left( {{9 \over 4}} \right) = {{45} \over 4}5(  

4

9

​  

)=  

4

45

​  

 is the number that we need to subtract to keep the equation unchanged.

Express the trinomial as a square of binomial, and combine the constants to get the final answer.

Therefore, the vertex \left( {h,k} \right)(h,k) is {{ - \,3} \over 2},{{ - \,65} \over 4}  

2

−3

​  

,  

4

−65

​  

.

Answer:

(x - 1 )^2 - 3

Step-by-step explanation:

( x - 1 )^2 + ( -3)

x^2 - 2x + 1 - 3

x^2 - 2x - 2

If a machine that works at a constant rate can fill 40 bottles of milk in 3 minutes, Then the machine will take approximately 18 minutes to fill 240 bottles.

Constant rate is a rate of change is constant when the ratio of the output to the input stays the same at any given point on the function.

Given that machine take 3 minutes to fill 40 bottles

So for 1 minute the machine fill \(\frac{40}{3}\) = 13.3333 bottles.

That is in 1 minute the machine fill approximately 14 bottles.

So the machine take a time to fill 240 bottles is \(\frac{240}{14} = 18.461\).

Thus the machine take approximately 18 minutes to fill 240 bottles.

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Answer:

Step-by-step explanation:

7b=63

b=9

Answer: Okay, the answer is x^2/68+(y+3)^2/17=1.

Step-by-step explanation: Step. 1 Complete the square for 4y^2+24y: 4(y+3)^2−36.

Step 2. You’ll need to substitute 4(y+3)^2−36 for 4y^2+24y in the equation x^2+4y^2+24y=32: x^2+4(y+3)^2–36=32.

Step 3. So you’ll need to move –36 to the right side of the equation by adding 36 to the both sides: x^2+4(y+3)^2=32+36.

Step 4 You add 32 and 36: x^2+4(y+3)^2=68.

Step 5. You divide each term by 68 to make the right side equal to one: x^2/68+4(y+3)^2/68=68/68.

And step 6. You’ll need to simplify each term in the equation in order to set the right side equal to 1. The standard form of an ellipse or hyperbola requires the right side of the equation be 1: x^2/68+(y+3)^2/17=1. I hope you download Math-way app to calculate this ellipse in standard form to be extremely helpful, please mark me as brainliest, and have a great weekend! :D

Answer:

A

Step-by-step explanation:

Answer:

450, 566 ; 450,082 ; 405,987

Step-by-step explanation:

Number of visitors in may = 450,082

Number of visitors in June = 450,566

Number of visitors in July = 405,987

Arranging the number of visitors from greatest to least(In descending order).

450,566 > 450,082 > 405,987

450, 566 ; 450,082 ; 405,987

The 20 questions test answers may a student mark 8192 ways.

What is the combinations?

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

Since there are 20 questions, and each question can be answered in if 7 questions mark correctly and 13 incorrectly then:

7 questions can be answered correctly.

13 questions can be answered incorrectly.

The 2 questions can be answered in

2 × 2 ways.

The 3 questions can be answered in 2×2×2 ways and so on.

So we have:

1 × 1 × 1 × 1 × 1 × 1 × 1 × 2¹³

= 8192

Hence, the 20 questions test answers may a student mark 8192 ways.

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The true response would be 15,488/7 square centimeters based on the information provided.

Square offers businesses a range of goods and services to help them complete sales transactions, use marketing strategies, and control their finances, inventory, and workforce.

The lateral surface (the curved portion of the cylinder) is added to the areas of a round top and bottom to figure out the surface surface of the cylindrical cheese wheel. The perimeter of the base (2πr, where r is the radius) as well as the height can be used to compute the lateral surface area. Each round top and bottom's surface area is πr².

Hence, the cheese wheel's overall surface area is:

(2πr × h) + (2πr²)

Inputting the values provided yields:

(2 × 22/7 × 22 × 16) + (2 × 22/7 × 22 × 22)

When we simplify and find the total area of the surface, we obtain:

15,488/7 square centimeters

As a result, 15,488/7 square centimeter of the cheese wheel are covered by the label.

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The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m is the slope. The equation of the line that is perpendicular to y = -2x + 4 and passes through the point (4, 2) is given by option D: y = -2x.

To determine which equation represents a line perpendicular to y = -2x + 4 and passes through the point (4, 2), we need to consider the slope of the given line. The equation y = -2x + 4 is in slope-intercept form (y = mx + b), where the coefficient of x (-2 in this case) represents the slope of the line.

Since we are looking for a line that is perpendicular to this given line, we need to find the negative reciprocal of the slope. The negative reciprocal of -2 is 1/2. Therefore, the slope of the perpendicular line is 1/2.

Now, we can use the point-slope form of a line to find the equation. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m is the slope.

Substituting the values (4, 2) for (x₁, y₁) and 1/2 for m, we get:

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

Simplifying this equation, we find:

y - 2 = (1/2)x - 2.

Rearranging the terms, we obtain:

y = (1/2)x.

Therefore, option D, y = -2x, represents the equation of the line that is perpendicular to y = -2x + 4 and passes through the point (4, 2).

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Hey there!

6x - 8y

= 6(6) - 8(-2)

= 6(6) + 8(2)

= 36 + 16

= 52

Therefore, your answer is: 52

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The calculations with the correct number of significant figures and units are as follows:

0.0001 = 1.0 x 10^-4 (Scientific notation with 1 significant figure)

2100 = 2100 (4 significant figures)

70.75 = 70.8 (3 significant figures, rounding up)

0.0120 = 0.012 (2 significant figures, trailing zeros are not significant)

500 = 500 (3 significant figures)

7.65 x 10^2 = 765 (3 significant figures)

1000 = 1000 (1 significant figure)

0.10 = 0.10 (2 significant figures)

6.023 x 10^23 = 6.02 x 10^23 (3 significant figures)

1,379,387 = 1,380,000 (4 significant figures, rounding up)

For unit conversions, the following calculation can be performed to determine the mass of a bar of gold:

We have,

Density of Au = 19.3 g/cm^3

Length = 6.0 inches = 6.0 inches x 2.54 cm/inch = 15.24 cm

Width = 4.0 inches = 4.0 inches x 2.54 cm/inch = 10.16 cm

Height = 2.0 inches = 2.0 inches x 2.54 cm/inch = 5.08 cm

Volume of the bar = Length x Width x Height

Volume = 15.24 cm x 10.16 cm x 5.08 cm = 780.6912 cm^3

Mass = Density x Volume

Mass = 19.3 g/cm^3 x 780.6912 cm^3 = 15,073.8816 g

Converting grams to kilograms:

Mass = 15,073.8816 g x (1 kg / 1000 g) = 15.0738816 kg

Therefore, the mass of the bar of gold is approximately 15.07 kg.

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Answer:

8

Step-by-step explanation:

800/100

= 8/1 or just 8

Answer:

8/1

Step-by-step explanation:

Convert the percent to a decimal.

800% => move the decimal two times to the right so,

8.00 as a decimal = 8/1 => 8