The statements can be arranged correctly as follows:
1. Word Form shows a number written in words.
2. Standard form shows a number written using digits.
3. Digit is one of the numerals from 0 to 9
4. Place value the position of a digit in a number, which determines its value.
5. Period each three-digit part of a whole number, separated by commas
6. Expanded form shows a number written as an addition statement
How to determine the termsWe can determine the terms by first understanding the mathematical meanings. Word form is a term used in math to denote expressions written in word B.
Also, the standard form is a way of shortening large numerical values using digits. Digits are single numbers that run between 0 to 9 and they make up the higher values of numbers.
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Write a quadratic function with zeros -9 and 7
The quadratic function with roots -9 and 7 is f(x) = x² + 2x - 63
What is the quadratic function with zeros -9 and 7?First, recall that a quadratic function has the form:
f(x) = ax² + bx + c
where a, b, and c are constants.
Given the roots of the quadratic function:
-9 and 7
x = -9 and x = 7 are the two distinct solutions to the quadratic equation.
Hence:
x + 9 and x - 7 are the factors of the quadratic equation.
( x + 9 ) ( x - 7 )
Expanding this expression Using FOIL method:
x( x - 7 ) + 9( x - 7 )
x² - 7x + 9x - 63
Collect and add like terms
x² + 2x - 63
Therefore, the function is f(x) = x² + 2x - 63.
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A water park has pools, slides, and rides that, in total, make use of 8.8 × 1 0 5 8.8×10 5 gallons of water. They plan to add a ride that would make use of an additional 51 , 000 51,000 gallons of water. Use scientific notation to express the total gallons of water made use of in the park after the new ride is installed.
[tex]9.31*10^5[/tex] gallons are the total gallons of water used by the water park after adding the new ride.
To express the total gallons of water used by the water park after adding the new ride in scientific notation, we need to add the two values together and then convert them to scientific notation.
[tex]8.8*10^5[/tex] gallons + 51,000 gallons = [tex]9.31*10^5[/tex] gallons
Therefore, the total gallons of water used by the water park after adding the new ride is [tex]9.31*10^5[/tex] gallons.
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The volume of a cube depends on the length of its sides. This can be written
in function notation as v(s). What is the best interpretation of ✓(2) = 8?
A. 2 sides of the cube have a total length of 8 feet.
B. A cube with side lengths of 2 feet has a volume of 8 cubic feet.
C. A cube with a volume of 2 cubic feet has side lengths of 8 feet.
OD. 2 of these cubes will have a total volume of 8 cubic feet.
Answer:
B. A cube with side lengths of 2 feet has a volume of 8 cubic feet.
v(s) = s^3, so v(3) = 2^3= 8
Autumn's Pumpkin Patch started the day with 432 pumpkins, each priced at $5. Most of
the pumpkins sold. At the end of the day, there were only 129 pumpkins left. How much
money did the pumpkin patch make today?
Answer:
It's very simple you just subtract 432 and 129. And you get 303. Then you just multiple 303 by 5 and you get 1515.
1515
Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Refer to the accompanying data set. Use a 0.01 significance level to test the claim that women and men have the same mean diastolic blood pressure.
The null and alternative hypothesis is represented by option A.
The test statistic is 0.153.
How to explain the informationWe want to test the claim that women and men have the same mean diastolic blood pressure.Let μ1 be the mean diastolic blood pressure for women and let μ2 be the mean diastolic blood pressure for men.
The t-statistic value will be:
= (69.81 - 69.53) / (✓10.46²/26 + 11.24²/26)
=0.153
Since p-value for two tail test=0.879 which is greater than =0.05(0.879>0.05) So we do not reject H0.
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Given a trapezoid with a height of 4.3 m and bases of 9.2 m and 3.2 m, what is the area of the trapezoid? Do not include units in your answer. Round your answer to the nearest tenth.
Answer:
26.5
Step-by-step explanation:
The formula for the area of a trapezoid is:
A = (1/2)h(b₁ + b₂)
where h is the height, b₁ and b₂ are the lengths of the parallel bases.
Substituting the given values:
A = (1/2)(4.3 m)(9.2 m + 3.2 m)
A = (1/2)(4.3 m)(12.4 m)
A = 26.52 m²
Rounding to the nearest tenth:
A ≈ 26.5
Therefore, the area of the trapezoid is approximately 26.5 square meters.
5. Is the bottom shelf parallel to the middle shelf? Explain. (2 points)
Answer:
Yes, the bottom shelf is parallel to the middle shelf. Angle 6 measures 120°, so angles 6 and 11 are congruent alternate exterior angles.
Hunter has a cylindrical cup of Cheerwine. Their cup has a volume of about 1356.48 cubic centimeters. The cup has a height of 12 cm. Using 3.14 for pi, what is the radius of the cup?
Group of answer choices
36 cm
3 cm
6 cm
18 cm
The radius of the cylindrical cup is 6 centimeters.
What is the radius of the cup?A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.
The volume of a cylinder is expressed as;
V = π × r² × h
Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )
Given that the volume of the cylindrical cup is 1356.48 cubic centimeters and the height is 12 cm.
We can substitute these values into the formula and solve for the radius:
V = π × r² × h
r = √( V / (πh) )
r = √( 1356.48 / ( 3.14 × 12) )
r = 6 cm
Therefore, the radius is 6cm.
Option C) 6cm is the correct answer.
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Which is the graph of g(x)=√x-16?
←
The graph of g(x) = √(x - 16) is given by the image presented at the end of the answer.
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The parent function in this problem is given as follows:
f(x) =√x
Which has vertex at the origin.
The function g(x) = √(x - 16) is equivalent to g(x) = f(x - 16), which is a translation right 16 units of f(x), according to the graph presented at the end of the answer.
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What is the midpoint of line segment Ab (-3,-5) (-1,-7)
Answer:
(-2, -6)
Step-by-step explanation:
Midpoint = (x1 + x2)/2, (y1 + y2)/2
= (-3 + -1)/2, (-5 + -7)/2
= (-4/2), (-12/2)
= (-2, -6)
URGENT!! ILL GIVE BRAINLIEST! ALONG WITH 100 POINTS
Use the normal distribution of SAT critical reading scores for which the mean is 515 and the standard deviation is 125. Assume the variable x is normally distributed. What percent of the SAT verbal scores are less than 675? If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 550?
The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 515, \sigma = 125[/tex]
The proportion of scores less than 675 is the p-value of Z when X = 675, hence:
Z = (675 - 515)/125
Z = 1.28
Z = 1.28 has a p-value of 0.8997.
Hence the percentage is 89.97%.
The proportion of scores greater than 550 is one subtracted by the p-value of Z when X = 550, hence:
Z = (550 - 515)/125
Z = 0.28
Z = 0.28 has a p-value of 0.6103.
1 - 0.6103 = 0.3897, hence the amount is given as follows:
E(X) = 1000 x 0.6103 = 610.
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(10x-23) how do i find x with 106 as an arc
I'm assuming you mean "How do I find the value of x such that the arc length of the circle defined by (10x-23) is 106?" So, there are two possible values of x that would give a circle with arc length 106: x ≈ 2.71 and x ≈ 1.89.
To find the value of x such that the arc length of the circle defined by (10x-23) is 106, we can use the formula for the arc length of a circle:
Arc Length = θr
where θ is the central angle in radians, and r is the radius of the circle.
In this case, we know the arc length is 106, and we need to find the value of x such that the radius is defined by (10x-23). Let's call this radius r.
We can rearrange the formula to solve for the radius:
r = Arc Length / θ
We also know that the central angle in radians is equal to the arc length divided by the radius.
So we can write:
θ = Arc Length / r
Substituting in the values we have:
θ = 106 / (10x-23)
Now we can solve for x. We know that the central angle for a full circle is 2π radians, so the central angle for a circle with radius (10x-23) is:
θ = (2π)(10x-23)
Setting this equal to our previous expression for θ, we have:
106 / (10x-23) = (2π)(10x-23)
Solving for x:
106 = (2π)(10x-23)(10x-23)
106 = (2π)(100x^2 - 460x + 529)
53 = π(100x^2 - 460x + 529)
53/π = 100x^2 - 460x + 529
100x^2 - 460x + (529 - 53/π) = 0
We can solve this quadratic equation using the quadratic formula:
x = [460 ± sqrt(460^2 - 4(100)(529 - 53/π))] / (2(100))
x ≈ 2.71 or x ≈ 1.89
Therefore, there are two possible values of x that would give a circle with arc length 106: x ≈ 2.71 or x ≈ 1.89.
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Find the perimeter of this shape
Answer:
3y+8x
Step-by-step explanation:
To solve this problem we first have to add similar terms
Adding like terms:
So let us add up the sides that have the same variable. Let us solve for the variable y first ->
[tex]4+y+2y-2\\\\(y+2y)+(4-2)\\\\3y+2[/tex]
Now we have the simplified form of the y. Now let us solve for x ->
[tex]6x+2+2x-4\\\\(6x + 2x) + (2 - 4)\\\\8x - 2[/tex]
Combine both expressions:
To combine these expressions we add the constants and leave the variables. (We do this because different variables cannot be added together)
[tex]8x - 2 +3y +2\\\\8x + 3y + (-2 + 2)\\\\8x+3y+0\\\\8x+3y[/tex]
So 3y + 8x is the asnwer
The world record in the long jump is 29 feet 4 inches. How many inches short of 10 yards is the record long jump?
The record long jump is 8 inches short of 10 yards.
We know that 1 yard is equal to 3 feet, so 10 yards is equal to 10 x 3 = 30 feet.
To find out how many inches short of 10 yards the record long jump is, we need to first convert 29 feet 4 inches to inches only.
We can do this by multiplying the number of feet by 12 (since there are 12 inches in a foot) and then adding the number of inches:
29 feet 4 inches = (29 x 12) + 4
= 348 + 4
= 352 inches
Now we can find out how many inches short of 10 yards the record long jump is:
30 feet = 30 x 12 = 360 inches
360 - 352 = 8
Therefore, the record long jump is 8 inches short of 10 yards.
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A sports ball has a diameter of 23 cm. Find the volume of the ball. Round your answer to 2 decimal places, and use 3.14 as an approximation of n cm³,
The volume of the sports ball is 6286.28 cm³
What is volume of a sphere?A sphere is round, has no edges, and is a solid shape. Examples of a sphere include; The playing ball, balloon, and even light bulbs .
A sphere is a 3-dimensional shape ,and it's therefore a solid shape.
The volume of a sphere is expressed as;
V = 4/3 πr³
where r is the radius of the sphere and v is the volume.
the radius of the sphere is half the diameter.
D = 2r
r = 23/2 = 11.5
therefore ;
V = 4/3 × 3.14 × 11.5³
V = 18858.85/3
V = 6286.28 cm³ ( 2 decimal place)
Therefore the volume of the ball is 6286.28 cm³
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500
9. A tennis ball manufacturer wants to estimate the mean circumference of tennis balls within 0.05 inch.
Assume the population of circumferences is normally distributed. Determine the minimum sample size
required to construct a 95% confidence interval for the population mean. Assume the population
standard deviation is 0.10 inch..
The minimum sample size required to construct a 95% confidence interval for the population mean is 16.
To determine the minimum sample size required to construct a 95% confidence interval for the population mean circumference of tennis balls within 0.05 inch, we need to use the formula for the margin of error:
Margin of error = Z* (σ/√n)
Where Z* is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.
Since we want a 95% confidence interval, Z* = 1.96 (from a standard normal distribution table).
We are given that σ = 0.10 inch and we want the margin of error to be 0.05 inch. Plugging in the values, we get:
0.05 = 1.96 * (0.10 / √n)
Solving for n, we get:
n = [(1.96 * 0.10) / 0.05]² = 15.36
We can't have a fractional sample size, so we round up to the nearest whole number. Therefore, the minimum sample size required is 16.
This means that the manufacturer needs to randomly select and measure the circumferences of at least 16 tennis balls to estimate the population mean circumference with 95% confidence and a margin of error of 0.05 inch.
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The coordinates of the point � G are ( 0 , 8 ) (0,8) and the coordinates of point � H are ( 8 , 8 ) . (8,8). What is the distance, in units, between the point � G and point � ? H?
The distance between the points G and H is D = 8 units
Given data ,
Let the distance between 2 points be represented as D
Now , let the first point be G ( 0 , 8 )
Let the second point be H ( 8 , 8 )
Now , let the distance between G and H be D , where
D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)
D = √ ( 0 - 8 )² + ( 8 - 8 )²
D = √64 units
D = 8 units
Hence , the distance is 8 units
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farmer gibson has a heard of 200 cows he sold 60 cows what percentage of his heard remains? Please hurry I need it today!
To find the percentage of Farmer Gibson's herd that remains after he sold 60 cows, we need to calculate the new total number of cows he has.
Number of cows remaining = Total number of cows - Number of cows sold
Number of cows remaining = 200 - 60
Number of cows remaining = 140
So, Farmer Gibson has 140 cows remaining in his herd.
To find the percentage of cows remaining, we can use the following formula:
Percentage = (Number remaining ÷ Total number) x 100
Plugging in the values we have:
Percentage = (140 ÷ 200) x 100
Percentage = 0.7 x 100
Percentage = 70%
Therefore, Farmer Gibson has 70% of his herd remaining after selling 60 cows.
~~~Harsha~~~
Number of sheets: 55 A) 10-1 What is the ratio of the total height in millimeters of 2 mm thick paper to the total height in millimeters of 23 mm thick papers? Number of papers: 56 B) 10-2 C) 10-3
If the number of papers is 56, the ratio of the total height in millimeters of 2 mm thick paper to the total height in millimeters of 23 mm thick paper is 2:23.
What is the ratio?The ratio is the relative size of two comparable quantities, values, or numbers.
Ratios are computed as the quotients of one value (the numerator) and another (the denominator).
We can depict ratios as decimals, fractions, percentages, or in their standard forms (:).
The total height in millimeters of 2 mm thick paper = 112 mm (56 x 2)
The total height in millimeters of 23 mm thick papers = 1,288 mm (56 x 23)
Ratio = 0.0869 (112 ÷ 1,288) or 2/23 or 8.69%.
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Drawn from Quiz 5 Prep Notes: 20.5) Suppose that the study in the amount of healing as measured in square mm of new tissue for the median difference between the methods of soaking the amputated injured newt limbs in a control versus a benzamil solution in the previous problem 20.4), yielded a 95% confidence interval of (-0.02, 0.16) mm? Interpret the meaning of the 95% confidence interval: 96% of what must be true? Select the correct order and number of sentence fragments below that wil express the correct interpretation of 95% confidence. Click and drag 8 sentence fragments from the left column to form a correct interpretation of the meaning of 95% confidence in the right column. Your selections must be in the correct order to read the interpretation as correct. ..to create the correct interpretation of confidence here Choose phrases from here... there is a 95% chance that 96% confidence means that will generate confidence intervals that bracket will form confidence intervals that fit within the confidence interval of (-0.02. 0.16) we have calculated there is a 95% chance that 95% confidence means that will generate confidence intervals that bracket will form confidence intervals that fit within the confidence interval of (-0.02, 0.16) we have calculated. has at least as much healing as was seen in for the median difference of healing in mm the true median difference the true mean difference all random samples drawn 95% of will exist within the confidence interval the sample median difference of new tissue formed in mm. between the methods of soaking in a control vs benzamil solution
The 95% confidence interval of (-0.02, 0.16) mm for the median difference between the methods of soaking the amputated injured newt limbs in a control versus a benjamin solution means that we are 95% confident that the true median difference of healing in mm will exist within the confidence interval of (-0.02, 0.16).
The 95% confidence interval of (-0.02, 0.16) mm means that there is a 95% chance that the true median difference in healing between the methods of soaking the amputated injured newt limbs in a control versus a benjamin solution falls within this range. This means that 95% of all random samples drawn will exist within this confidence interval, and we can be confident that the methods used in this study have at least as much healing as was seen in the sample median difference of new tissue formed in mm. Therefore, with 96% confidence, we can say that the true median difference in healing between the two methods is somewhere within this range. Methods used to generate confidence intervals that bracket the true median difference will form confidence intervals that fit within the confidence interval of (-0.02, 0.16) we have calculated.
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the sonar system then detects a sunken ship 1500 meters ahead, with an angle of elevation of 19° to the highest part of the sunken ship. how many meters must the submarine rise to pass over the sunken ship?
Step-by-step explanation:
Tan Φ = opposite leg / adjacent leg
tan 19 = height / 1500
1500 * tan 19 = height = 516 m <==== must rise this much
pedro is on a bike. he rides 7 miles south and 5 miles east. how many miles would he have saved if he instead took the shortest route?
The number of miles that he would have saved instead would be = 8.6 miles
How to calculate the miles he would have saved?The amount of miles he traveled south = 7 miles
The amount of miles he traveled east = 5 miles
To calculate the number of miles he would have saved, the Pythagorean formula is used;
That is :
C² = a²+ b²
a = 7
b =5
c² = 7²+5²
= 49+25
= 74
c = √74
= 8.6 miles
Therefore, he would have travelled 8.6 miles instead of 12 miles.
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solve for x in the diagram
Answer:
see attatched picture
Step-by-step explanation:
Your generous wealthy aunt wants to ensure you have enough money to cover rent and food while you go to college so you don’t need to work while you’re in classes. Together you decide $18,000 per year is sufficient to cover your basic needs. How much does your aunt need to invest in a bond mutual fund that yields 3.0% in order for it to provide $18,000 a year for you?
Your close relative has to contribute $17,430 in a bond shared finance that yields 3.0% for it to supply $18,000 a year for you.
How to Solve the Problem?To calculate the sum that your close relative has to contribute in a bond common finance to supply you with $18,000 per year, you wish to utilize the equation for the display esteem of an annuity.
PV = PMT * (1 - (1 + r)^(-n)) / r
where:
PV = display esteem
PMT = installment sum (in this case, $18,000 per year)
r = intrigued rate (3.0%)
n = number of periods (in this case, 1 year)
Substituting the values into the equation:
PV = $18,000 * (1 - (1 + 0.03)^(-1)) / 0.03
PV = $18,000 * (1 - 0.9709) / 0.03
PV = $18,000 * 0.0291 / 0.03
PV = $17,430
Subsequently, your close relative has to contribute $17,430 in a bond shared finance that yields 3.0% for it to supply $18,000 a year for you.
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Let f(x) = g(h(x)) = (√2x+5)/2x. Find two sets of possible formulas for g(x)
and h(x), assuming that g(x) does not equal x and h(x) does not equal x. There may be more than one possible answer.
.47/100+3/250=/1000+12/1000
Answer:is this actually a question!
Step-by-step explanation:
A rectangular prism has a length of 5 cm, a width of 212 cm, and a height of 112 cm.
Which expressions can be used to find the volume of the prism?
Select each correct answer.
Responses
5∙2 1/2∙1 1/2
12 1/2∙1 1/2
1 1/2(5+2 1/2)
1/2(12 1/2∙1 1/2)
Fernando wants to know how much interest he will earn on the $4000 he puts into a savings account. He has the interest rate. What other information does he need to know?
Answer:
the time period, and what compounding is usedStep-by-step explanation:
You want to know what else Fernando needs to know to figure how much interest he will earn on $4000, if he has the interest rate.
InterestThere are two interest formulas. One is for simple interest, and one is for compound interest. So, one bit of information Fernando needs is whether interest is being compounded.
The formulas are ...
I = P·r·t . . . . . . . simple interest
I = P((1 +r/n)^(nt) -1) . . . . . . compound interest
If Fernando knows the invested amount P and the interest rate r, then he needs to know 'n' and 't' to be able to choose and use the correct interest formula.
Fernando needs to know ...
the time period of concernthe number of times per year interest is compoundedThe sum of two consecutive numbers is
27. Find the two numbers.
Answer: 14 and 14
Step-by-step explanation:
So u would Since 13 and 14 are both consecutive integers and their sum is 27, we have our answer.