The dimensions of the rectangular prism with the volume 33x cubic units are 11units, 9units, 4 units.
As given in the question,
Dimension of the rectangular prism in form of x are :
( x - 3 ) , ( x - 1 ) , and ( x - 8 )
Volume of the rectangular prism = 33x cubic units
⇒ ( x - 3 )( x - 1 )( x - 8 ) = 33x
⇒ ( x² -4x + 3 )( x - 8) = 33x
⇒ x³ -12x² + 35x -24 = 33x
⇒ x³ -12x² + 2x -24 = 0
⇒ x² ( x - 12 ) + 2 ( x - 12 ) = 0
⇒ ( x - 12 )( x² + 2 ) = 0
⇒ x = 12 or x = √ -2
Dimensions cannot be square root of negative.
⇒ x = 12
x - 3 = 9 units
x -1 = 11 units
x - 8 = 4 units
Therefore, the dimensions of the rectangular prism are 9 units, 11unitsm and 4 units.
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Maria's plant grew 3 1/4 inches every month for 2 1/2 months. How many inches did Maria's plant grow during that time?
Answer: 8.125 inches
Step-by-step explanation: Ok so if the plant grew 3.25 inches every month, and there were 2.5 months, you need to multiply 3.25 by 2.5 to get the total amount of growth. So that would be 8.125.
Hope that helped!
The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught. Step 2 of 2: Suppose a sample of 782 suspected criminals is drawn. Of these people. 273 were captured. Using the data, construct the 98% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list. Round your answers to three decimal places.
The confidence interval is (0.309, 0.389).
Calculate a 98% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list.
Sample size, n = 782
Sample proportion, p = x/n = 0.349105
Confidence level, 1 - α = 98% = 0.98 Implies
Level of significance, α = 0.02
At α = 0.02, the two-tailed critical value from the z-table, Zα/2 = 2.33
Then, the 98% confidence interval is,
It gives, 0.309≤ p ≤0.389
Lower endpoint = 0.309
Upper endpoint = 0.389
We are 98% confident that the proportion of all suspected criminals who were captured is within the confidence interval. If we were to take a large number of random samples of size 782, 98% of the resulting confidence intervals would contain the true proportion of all suspected criminals who were captured.
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An investment of $9,875 earns 4. 8% interest compounded monthly over 12 years. Approximately how much interest is earned on the investment?.
Using the compound interest formula, we know that $7,672 is the interest on investments earned.
What is compound interest?The yearly interest rate is raised to the number of compound periods minus one, and the starting principal amount is multiplied by both of these factors.
The resulting value is subsequently deducted from the loan's entire original amount.
So, interest earned on investment:
A = 9,875 (1 + 0.048/12)^ 12(12)
A = $ 15,547
Interest on investments is the money received:
= $ 15,547 - $ 9,875
= $ 7,672
Therefore, using the compound interest formula, we know that $7,672 is the interest on investments earned.
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Complete question:
An investment of $9,875 earns 4.8% interest compounded monthly over 12 years. approximately how much interest is earned on the investment?
a. $4,740
b. $7,458
c. $7,672
d. $17,567
what solution value does not satisfy the compound inequality x – 7 < 17 or –6x > 36? question 2 options: a) x
The solution of compound inequalities is -6 < x < 24.
A compound inequality is a sentence that contains two inequality statements connected by the words "or" or "and." The conjunction "and" denotes that both statements of the compound sentence are true at the same time. It is the intersection or overlap of the solution sets for the individual statements. "Or" indicates that the entire compound sentence is true if either statement is true. It is the union or combination of the solution sets for each individual statement. A conjunction is a compound inequality that contains the word "and."
Inequalities are expressions that do not have an equal sign between them.
Given,
X - 7<17or-6x>36
First,
x - 7 < 17
x < 17 + 7
x < 24
Similarly,
-6x >36
x < [tex]\frac{-36}{6}[/tex]
x < -6
Thus, compound inequality's solution is -6 < x < 24
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Kaleb deleted 20 songs from his MP3 player. If the ratio of songs he deleted to songs he
kept was 10:3, how many songs did he originally have on his MP3 player?
If he deleted 10 songs to every 3 he kept, then he originally had 26 songs
Graph each function and identify its domain, range, intercepts, asymptotes, and holes.
Thank you! :)
Answer: The domain is : (-∞,5)∪(5,∞)
there is no x intercepts
y-intercept= (0,-29/5)
asymptotes= x=5, no horizantal, oblique y=x-5
there is no holes
range= (-∞,-4]∪[4,∞)
Step-by-step explanation:
PLS HELP ASAP!!!! 35pts!!
The hypotenuse - leg congruency can be applied in both right triangles.
How to find congruent triangles?Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
If the hypotenuse and a side of a right- angled triangle is equivalent to the hypotenuse and a side of the second right- angled triangle, then the two right triangles are said to be congruent by RHS rule.
In other words, if the hypotenuse and a leg of a right triangle are each congruent with the corresponding hypotenuse and leg of another right triangle, then the triangles are congruent.
Hence, the legs of the right triangle are congruent and one of the legs are congruent.
Therefore, the hypotenuse - leg congruency can be applied.
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What is the range of this relation?
Jack took Diane out to dinner to celebrate her birthday. The total bill for the dinner was $62.80. Jack wants to tip the waiter exactly 15%. How much will Jack tip the waiter?
The amount of the tip that Jack gave to the waiter will be $9.42.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Jack took Diane out to supper to praise her birthday. The all out bill for the supper was $62.80. Jack needs to tip the server precisely 15%.
The amount of the tip will be given as,
⇒ 15% of $62.8
⇒ 0.15 x $62.8
⇒ $9.42
The amount of the tip that Jack gave to the waiter will be $9.42.
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a researcher writes down in a notebook the arrival times of different city buses at a bus stop during different weather conditions. which kind of study is this?
The times that buses arrive at bus stops in various cities and in various climates are noted by a researcher in a notebook. This study is an observational one. Here option D is the correct answer.
It is an observation because it involves systematically noting people's actions, things, and occurrences without engaging in conversation or other interactions. In observational studies, the impact of a risk factor, diagnostic test, therapy, or other intervention is observed without an attempt to alter who is or is not exposed to it.
Two categories of observational studies are cohort studies and case-control studies. It cannot be a single-blind experiment, nor can it be a double-blind experiment since it is not an experiment.
Single-blind refers to a subject or an assessor. When a study is double-blind, neither the patient nor the outcome evaluator is aware of who received the prescription. It is not a survey because it relies on interviews with a representative sample of people as the main way of gathering data.
Complete question:
A researcher writes down in a notebook the arrival times of different city buses at a bus stop during different weather conditions. Which kind of study is this?
A - observational
B - survey
C - single-blind experiment
D - double-blind experiment
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Drew painted his uncle's barn on Saturday. It took him 8 hours to paint the whole barn, and his uncle paid him 224 dollars for his work. What was Drew's pay rate, in dollars per hour?
Answer:
$28/hour
Step-by-step explanation:
224 ÷ 8 = 28
How can the triangles be proven similar by the SSS similarity theorem?
Answer:
I Think its b
Step-by-step explanation:
(show that the ratio UV_XY and WV_ZY are equivalent.)
*3rd thing*
if it is wrong (which i dont think it is) then show me a study guide or some way to learn more about it, hope this helps
let e1 be the event that the second coin comes up tails and e2 be the event that two, and not three, heads come up in a row. drag the probability values from the right column and drop them in the corresponding events of left column.
EVENT 1 has a probability value of 0.5.
EVENT 2 has a probability value of 0.5.
There is an equal chance of getting a HEAD or a TAIL when flipping a fair coin.
A coin has two faces: Head and Tail, and the total probability is always 1
1/2 = 0.5 is the likelihood of getting a head.
1/2 = 0.5 is the probability of receiving a tail.
When the coin is tossed for the first time, E1 is the event when TAIL comes up.
When the coin is tossed a second time, E2 represents the circumstance in which HEAD appears.
EVENT 1 has a probability value of 0.5.
EVENT 2 has a probability value of 0.5.
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Can someone check this plsss
Study the pattern in the table. Tell whether the relationship between x and y is linear, exponential, or neither, and explain your answer. If the relationship is linear or
exponential, write an equation for it.
an office typically orders 60 ink refills at a time. the company estimates that handling costs are 40% of the $10 unit cost and the monthly demand is around 20 units. the assumptions of the basic eoq model are applicable. what would be the cost to order?
Cost to order as per the economic order quantity model is equal to 10units.
As given in the question,
Demand of units per month = 20 units
Ordering cost = $10 unit
Carrying cost = 40% of 10
= (40 /100) × 10
= $4
Economic order quantity model ( EOQ)
= √[ 2 × ( Demand rate ) × ordering cost ]/ carrying cost
Substitute the value we get,
= √ ( 2 × 20 × 10 )/ 4
= √400 / 4
= √100
= 10 units.
Therefore , as per the economic order quantity (EOQ) model cost to order is for 10 units.
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Show your work 0.4(20-10m) = 2.5 -2m -12.5
Answer:
give the guy under me a brainlist lol
Step-by-step explanation:
my question is how do you write a simplified expression that is equivalent to 7/8+3/8x-1/4y+3/4y-1/2?
Answer:
1/8(3x+4y+3)
Step-by-step explanation:
kennedy needs to order some new supplies for the restaurant where she works. the restaurant needs at least 512 spoons. there are currently 264 spoons. of each set on sale contains 6 spoons, what is the minimum number of sets of spoons kennedy should buy?
Kennedy needs purchase at least 42 sets of spoons.
Explain the term inequality of numbers?An algebraic expression with two values that are not equal is represented by an inequality. A sign of inequality can be used to show that one of the two variables is larger than, greater than or comparable to, less than, or equal to another value.The minimum set of spoons needed in the restaurant = 512 spoons.
Available spoons = 264.
Each set on the sale has 6 spoons.
Let the minimum number of spoon set required be 'x'.
Then,
6x + 264 ≥ 512
Solving the in equality.
6x ≥ 512 - 264
6x ≥ 248
x ≥ 248/6
x ≥ 41.33
Thus, Kennedy needs purchase at least 42 sets of spoons.
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a right triangle has a hypotenuse of length 3 units and one side of length 2 units. what is the area of the triangle?
The area of the triangle is 3 units^2. Since the area is equal to
hside * side/ 2.
Define area.
The measure of a region's size on a plane or curved surface is called area. While surface area refers to the area of an open surface or the boundary of a three-dimensional object, the area of a plane region or plane area refers to the area of a form or planar lamina.
Area is defined as the total amount of space occupied by a flat (2-D) surface or the shape of an object. On a sheet of paper, draw a square with a pencil. It is a two-dimensional figure. The area of a shape on paper is the area it occupies.
Solution Explained:
Given,
Length of Hypotenuse = 3units
One side = 2units
Area = (Length of Hypotenuse X Length one side) / 2
= (3 X 2) / 2
= 3units^2 (after calculation)
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omg please help me with the ones with the red dot t’s for my math geometry class
read the first five results and summarize the models they describe. choose one you find interesting, and determine how it is similar to the nist sp 800-100 model. how is it different?
Answer: Both the National Institute of Standards and Technology (NIST)
Step-by-step explanation:
mrs.rockwell lost money on an investment at a rate of $4 per day. what is the change in her investment, due to the lost money, after 4 weeks?
The change in her investment, due to the lost money is $112
How to determine the amount of money lost to the investment?From the question, we have the following parameters that can be used in our solution:
Rate of loss = $4 per day
Duration = 4 weeks
From the above parameter, we can calculate the amount of money lost to the investment using:
Amount lost = Duration * Rate of loss
Substitute the known values in the above equation
So, we have the following equation
Amount = 4 weeks * $4
Convert weeks to days
Amount = 28 * $4
Evaluate the quotient
Amount = $112
Hence, the amount is $112
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a group of n people plays a game. each person puts their name on a slip of paper in a hat, and then picks a name randomly from the hat (without replacement). what is the standard ceviation of the number x of people who pick their own name (assume n≥2)?
Given that each individual has a [tex]\frac{1}{n}[/tex] chance of receiving their own name, we may indicate whether or not person I received their own name by using a sequence of n identically distributed Bernoulli random variables with
[tex]P=\frac{1}{n}[/tex] .
The total number of people who received their own name is the sum of these Bernoullis. The linearity of expectation causes the expected value of the sum to equal the sum of their respective expected values.
Since each summand has expected value [tex]\frac{1}{n}[/tex] and there are n of them, the expected value is one.
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a square in the x-y plane in free space has a point charge of q at comer (a/2,a/2) and the comer (a/2,-a/2) and a point charge of -q at (-a/2, a/2) and (-a/2, -a/2). a) find the electric potential at any point along the x-axis. b) evaluate v at x
Electrical potential at any point along the x-axis is V = Q/2πε0(1/R1 − 1/R3) and V at x is Vx = 0.55Q/πε0a
Given info,
A square in the x-y plane in free space has a point charge of q at comer (a/2,a/2) and the comer (a/2,-a/2) and a point charge of -q at (-a/2, a/2) and (-a/2, -a/2).
Let,
V = Q/4πε0R1 + Q/4πε0R2 + −Q/4πε0R3 + −Q/4πε0R4
= Q/2πε0(1/R1 − 1/R3)
With,
R1 = √[(x - a/2)² + (a/2)²]
R3 = √[(x + a/2)² + (a/2)²]
At x = a/2,
R1 = a/2
R3 = a√5/2
Vx = 0.55Q/πε0a.
Therefore, Electrical potential is V = Q/2πε0(1/R1 − 1/R3) and V at x is Vx = 0.55Q/πε0a
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What are advantages and disadvanteges when using percent to measure change?
Answer:
Step-by-step explanation:
Percentages are a powerful way to compare samples with different numbers of observations. By standardising measures using a scale of 0 to 100, samples can be compared quickly and easily. Any graph of the data, however, must include the full range of 0 to 100 to ensure that false impressions are not created.
5. the chi-square test for goodness of fit - no difference from a known population suppose you are reading a study conducted in the year 2000 about welfare recipients in the united states. the authors report the following frequency data on the household size of the 1,844 welfare recipients in their random sample: observed frequencies household size 5-or-more-person 4-person 3-person 2-person 1-person 203 277 301 550 513 you wonder if welfare recipients tend to live in different-sized households than the us population at large. you obtain the following data from the 2000 census: percent distribution of us households by size household size 5-or-more-person 4-person 3-person 2-person 1-person 10.83% 14.20% 16.53% 32.63% 25.81% [source: hobbs f., & Stoops, N. (2002). Census 2000 special reports: Demographic trends in [Source: the 20th century. U.S. Census Bureau.] You use a chi-square test for goodness of fit to see how well the sample of welfare recipients fits the census data. What is the most appropriate null hypothesis? O The distribution of household sizes among welfare recipients is the same as that provided by the census data. The distribution of household sizes among welfare recipients is equal across the five household-size categories. O The distribution of household sizes among welfare recipients is different from that provided by the census data. O The distribution of household sizes among welfare recipients is not equal across the five household-size categories. Fill in the missing values in the following table indicating the expected frequencies in each category for a sample size of 1,844, if the null hypothesis is true: Expected Frequencies Household Size 5-or-more-person 4-person 3-person 2-person 1-person 475.94 304.81 601.70 The chi-square statistic has been calculated for you: x2 = 8.31. The distribution of the chi-square statistic has degrees of freedom. Use the following Distributions tool to find the critical value. Chi-Square Distribution Degrees of Freedom = 4 4 10 11 12 13 14 With the level of significance a = .01, the critical value is Because the chi-square statistic x2 is the critical value, you the null hypothesis. Therefore, you conclude that the proportions of welfare recipients in the five household-size categories differ from the corresponding proportions for all U.S. households.
The confidence interval for the given ANOVA test to calculate the average typing speed be, (144.83 , 155.17) and the margin of error of the poll be, ±5.17
On Subtracting 1 from your sample size, we get
150 – 1 = 149.
On Subtracting confidence level from 1, and then divide by two.
(1 – .95) / 2 = 0.025
Now, df = 149 and α = 0.025
from the table at df = 149 we got 2.262.
Divide your sample standard deviation by the square root of your sample size.
28 / √(150) = 2.28
Now, 2.262 × 2.28 = 5.17
So, the confidence interval be,
(150 - 5.17 , 150 + 5.17) = (144.83 , 155.17)
Hence, the confidence interval for the given ANOVA test to calculate the average typing speed be, (144.83 , 155.17) and the margin of error of the poll be, ±5.17
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Find the measure of A:
A
15x
31x-2
Answer:
30
Step-by-step explanation:
Triangles add up to 180.
Your known sides are: 15x, 31x-2, and 90 (the square on the corner of the angle tells you that it's a right angle or 90 degrees.)
First make an equation to find X
this looks like: 15x+31x-2+90=180
I just added the sides we know and set them to equal 180. Because triangles add up to 180.
Now solve this by first combining like terms
15x+31x-2+90=180 (do the numbers with x's) so 15x+31x
46x-2+90=180 (now combine the numbers without X's) so -2+90
46x+88=180 (now since 88 is positive, do the opposite and subtract it from 180. This is because 180 is on the other side of the = sign.)
46x=92 (now since 46x means 46 times x, you do the opposite of multiplication and divide 92 by 46.
This gives you x=2
Now the last thing you need to do is solve for angle A
Angle A says "15x" so you can substitute our x value (2) for the x
This looks like 15(2) 15 times 2 is 30
so 30 should be your answer
help me with math pls im almost done with it for the week...................
The expression (5/3)x + (5/9)y is equivalent to the given expression. which is the correct answer would be an option (A).
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
The expression is given in the question as:
(2/3)x - (4/9)y + x + y
Rearrange the terms in the above expression,
(2/3)x + x - (4/9)y + y
Combine the likewise terms,
(5/3)x + (5/9)y
Therefore, the expression (5/3)x + (5/9)y is equivalent to the given expression.
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use the appropriate normal distribution to approximate the resulting binomial distributions. a fair coin is tossed 130 times. what is the probability of obtaining between 55 and 69 tails, inclusive? a) 0.7523 b) 0.7134 c) 0.7221 d) 0.7179 e) 0.7494 f) none of the above.
The probability is 0.6962 for the given standard deviation.
What is standard deviation?
Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.
Main body:
X - Binomial(n = 130, p = 0.5)
Binomial can be approximated to normal with: μ = np = 130*0.5 = 65
σ = √np(1 − p) - = √130* (0.5)(1 − 0.5)
σ = 5.7
P(55 ≤ X ≤ 69 )
Since we are approximating a discrete binomial distribution by continuous normal distribution, values between 54.5 and 68.5 both approximate to 55. Thus, "between 55 and 69" corresponds to continuous normal distribution with P(54.5 < X 68.5) after continuity correction.
Normal Distribution, x₁ = 54.5, x2 = 68.5, µ = 65, σ = 5.7
We convert this to standard normal using z =
z₁ = 54.5-65/ 5.7 ≈ - 1.84
z₂ = 68.5-65/ 5.7 ≈ 0.614
P(54.5 < X < 68.5) = P(- 1.84 < Z < 0.614)
= P(Z < 0.614) − P(Z <- 1.84)
= 0.7291 - 0.0329 (from z-table)
= 0.6962
Hence the probability is 0.6962
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