A storage pod has a rectangular floor that measures 21 feet by 9 feet and a flat ceiling that is 7 feet above the floor. Find the area of the floor and the volume of the pod.
Answer:
area: 189 ft²volume: 1323 ft³Step-by-step explanation:
The area of the rectangular floor is the product of its length and width:
A = LW = (21 ft)(9 ft) = 189 ft²
The volume of the pod is the product of that floor area and the height:
V = Bh = (189 ft²)(7 ft) = 1323 ft³
The area of the floor is 189 ft²; the volume of the pod is 1323 ft³.
There are 16 sixth graders and 20 seventh graders in the Robotics Club. For the first project, the club sponsor wants to organize the club members into equal-size groups. Each group will have only sixth graders or only seventh graders. How many students will be in each group if each group has the greatest possible number of club members?
Apply distributive property to create an equivalent expression 6(5r-3)=
Answer:
30r-18
Step-by-step explanation:
6*5=30
6*3=18
Answer:
30r-18
Step-by-step explanation:
Type the standard form of three hundred thousand two hundred one
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
Standard form is numbers only.
Examples of standard numbers are 4, 225, or 9,002
A thousands number has 4 digits.
A hundreds number has 3 digits.
A tens number has 2 digits.
A regular number has 1 digit (itself).
Three hundred means 300.
Three hundred thousand, would be 300 times 1,000 (one thousand), or adding 3 zeros.
Two hundred is 200.
One is 1.
300 times 1,000 is 300,000.
300,000 and 200 is 300,200.
If the ones digit has a 1, then the number is 300,201.
Three hundred thousand, two hundred one written in standard form is 300,201.
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
Three hundred thousand, two hundred one written in standard form is 300,201.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
A thousand number has 4 digits.
A hundred number has 3 digits.
A tens number has 2 digits.
A regular number has 1 digit (itself).
Three hundred means 300.
Three hundred thousand would be 300 times 1,000 (one thousand), or adding 3 zeros.
Two hundred is 200.
One is 1.
300 times 1,000 is 300,000.
300,000 and 200 is 300,200.
If the one digit has a 1, then the number is 300,201.
Three hundred thousand, two hundred one written in standard form is 300,201.
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5(x + 3) - (9x - 4)
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf - 4x + 19}}}}[/tex]
Step-by-step explanation:
[tex] \sf{5(x + 3) - (9x - 4)}[/tex]
Distribute 5 through the parentheses
⇒[tex] \sf{5x + 15 - (9x - 4)}[/tex]
When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression. Also, remove the parentheses
⇒[tex] \sf{5x + 15 - 9x + 4}[/tex]
Collect like terms
⇒[tex] \sf{5x - 9x + 15 + 4}[/tex]
⇒[tex] \sf{ - 4x + 15 + 4}[/tex]
Add the numbers : 15 and 4
⇒[tex] \sf{ - 4x + 19}[/tex]
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If there are 17.5 grams of sugar in 225 grams of an aqueous sugar solution, the percent-mass sugar is ______ and the percent-mass water is ______ . Express both answers to the correct number of significant figures.
Answer:
7.77%(m/m) ; 92.22%(m/m)
Step-by-step explanation:
Given that:
17.5 grams of sugar in 225 grams of an aqueous sugar solution
Percentage by mass of A in a solution (mass percent) = (mass of A / total mass of solution) × 100
Hence,
Percentage by mass of sugar:
= (mass of sugar / total mass of solution) * 100
= (17.5 / 225) × 100
= 0.0777777 × 100 = 7.77%(m/m)
Mass of water(solvent) = (225 - 17.5)g = 207.5g
= (207.5 / 225) × 100
= 0.922222 × 100 = 92.22%(m/m)
The bill in a restaurant is $102.25. A tip of 20% is added to the bill. What id tyhe final amount paid?
Answer: $117.59
Step-by-step explanation:
if each hash mark represents a spacing of 10 in which of the following ranges of values would you find |x|
Answer:
B, Between -40 and -50
Step-by-step explanation:
Because, X lies between hask mark 4 and 5 to the left of 0, which would make it -40 and -50.
List the new coordinate of point J' when the figure is reflected over the y-axis.
Answer: (-4, -3)
Step-by-step explanation:
The original coordinate of J is (4, -3)
Since it is reflex over y-axis, the y value remains.
For the x value, it is originally 4 units away from the y-axis positively, thus, after reflexing, it will be 4 units away from the y-axis negatively.
The new coordinate of J' is (-4, -3)
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A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8 ounces, the company wants the packages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sample of 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces. Suppose that in a particular sample of 50 packages, the mean amount dispensed is 8.171 ounces, with a sample standard deviation of 0.052 ounce.1. Is there evidence that the population mean amount is different from 8.17 ounces? (Use a 0.01level of significance.)2. State the null and alternative hypotheses.H0:μ ( ≥, ≤, =, <, >,≠ ) ________H1:μ ( ≥, ≤, =, <, >,≠ ) ________(Type integers or decimals.)3. The critical value(s) is(are) _____(Round to four decimal places as needed. Use a comma to separate answers as needed.)4. The test statistic is _______(Round to four decimal places as needed.)5. Reject/ Do not reject H0. There is sufficient/insufficient evidence to conclude the population mean amount is different from 8.17ounces.6. The p-value is _______(Round to four decimal places as needed.)7. Interpret the meaning of the p-value. Choose the correct answer below.A. The p-value is the probability of obtaining a sample mean that is equal to or more extreme than 0.001 ounce below 8.17if the null hypothesis is false.B. The p-value is the probability of obtaining a sample mean that is equal to or more extreme than 0.001 ounce away from8.17 if the null hypothesis is true.A. The p-value is the probability of obtaining a sample mean that is equal to or more extreme than 0.001ounce aboveB. The p-value is the probability of not rejecting the null hypothesis when it is false.
Answer:
We conclude that the mean amount packaged is equal to 8.17 ounces.
Step-by-step explanation:
We are given that in a particular sample of 50 packages, the mean amount dispensed is 8.171 ounces, with a sample standard deviation of 0.052 ounces.
Let [tex]\mu[/tex] = population mean amount packaged.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 8.17 ounces {means that the mean amount packaged is equal to 8.17 ounces}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 8.17 ounces {means that the mean amount packaged is different from 8.17 ounces}
The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean amount dispensed = 8.171 ounces
s = sample standard deviation = 0.052 ounces
n = sample of packages = 50
So, the test statistics = [tex]\frac{8.171-8.17}{\frac{0.052}{\sqrt{50} } }[/tex] ~ [tex]t_4_9[/tex]
= 0.1359
The value of t-test statistics is 0.1359.
Also, the P-value of test-statistics is given by;
the meaning of the p-value is that the p-value is the probability of obtaining a sample mean that is equal to or more extreme than 0.001 ounces away from8.17 if the null hypothesis is true.
P-value = P( [tex]t_4_9[/tex] > 0.136) = More than 40% {from the t-table}
Since the P-value of our test statistics is more than the level of significance of 0.01, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the mean amount packaged is equal to 8.17 ounces.
PLZ HURRY Yummy donuts gave 2 dozen chocolate donuts and 6 donut jelly donuts to the school.how many donuts did they give?
Answer:
they gave 18 donuts to the school.
Answer:
2 dozen= 24 + 6 = 30 donut.
What is the scientific notation of 0.0038
Answer: 3.8 * 10^-3 (10 to the negative third power)
Step-by-step explanation:
First, you would find the leading digit which is 3. Then, include the following digits after the decimal. The following digit is 8 so you have 3.8. After that, you count how many places the decimal point would move until it's after three. (3 places) And since the number is smaller than 1, the exponent is negative.
calculate the area of area of a rectangular with a base of 10cm and a height of 6cm
Answer:
[tex]\Huge \boxed{\mathrm{60 \ cm^2 }}[/tex]
Step-by-step explanation:
Area of a rectangle is length × width.
The length of the rectangle is 10 cm.
The width of the rectangle is 6 cm.
[tex]\Rightarrow 10 \cdot 6 \\\\\\ \Rightarrow 60[/tex]
The area of the rectangle is 60 cm².
Answer:
60cm is the answer
Step-by-step explanation:
Area of a rectangle is length × width.
so..... The length of the rectangle is 10 cm.
And the width of the rectangle is 6 cm.
so... 10x6=60 cm
One integer is 7 more than another. Their product is 98. Find the integers,
Answer:
- 14, - 7 or 7, 14
Step-by-step explanation:
Let the the two integers be x and (x + 7)
[tex] \therefore \: x(x + 7) = 98 \\ {x}^{2} + 7x - 98 = 0 \\ {x}^{2} + 14x - 7x - 98 = 0 \\ x(x + 14) - 7(x + 14) = 0 \\ (x + 14)(x - 7) = 0 \\ (x + 14) = 0 \: or \: (x - 7) = 0 \\ x = - 14 \: or \: x = 7 \\ \\ when \: x = - 14 \\ x + 7 = - 14 + 7 = - 7 \\ \\ when \: x = 7 \\ x + 7 = 7 + 7 = 14 \\ [/tex]
Hence the required integers are - 14, - 7 or 7, 14
Please Help! I'm Stuck!
Answer:
The area of P is 9 times the area of Q
Step-by-step explanation:
From P to Q
The side lengths are
6 : 2
Divide each side by 2
3:1
From length to area we square the scale factor
3^2 : 1^2
9 : 1
P to Q area is 9 to 1
The area of P is 9 times the area of Q
If 2x + 5 = -25 and -3m - 6 = 48, what is the product of x and m?
Stefen earns $88 in 8 hours. At this rate, how many dollars will he warn in 40 hours
Answer:
$440
Step-by-step explanation:
You need to find the unit rate by dividing how much he earned (88)by how many hours he worked (8) which equals $11 per hour.Then you take the unit rate (11) and multiply it by 40 which equals $440.
Find the indicated side of the
right triangle.
Answer:
?=9
Step-by-step explanation:
We have a special right triangle, the 45-45-90 triangle.
In a 45-45-90 triangle, the side lengths are x, and the hypotenuse is x√2.
Since we know that the side length is 9, this means that:
[tex]x=9\\\text{Hypotenuse}=x\sqrt2\\\text{Hypotenuse}=9\sqrt2[/tex]
The ? is 9.
Answer: 9
Step-by-step explanation:
( -8x + 3x 4 ) - ( -7x - 6x 4 )
Answer:
9x^4 -x
Step-by-step explanation:
( -8x + 3x^4 ) - ( -7x - 6x^4 )
Distribute the minus sign
( -8x + 3x^4 ) +7x + 6x^4
Combine like terms
3x^4 + 6x^4 -8x +7x
9x^4 -x
Answer:
x + 9x^4
Step-by-step explanation:
There is some confusion here. You likely meant by "3x 4" the power term 3x^4 and by "6x 4" the power term 6x^4. " ^ " indicates exponentiation.
Step 1: Eliminate the parentheses. Simply drop them from the first term.
The first term becomes -8x + 3x^4 and the second term becomes 7x + 6x^4.
Now combine like terms:
-8x + 3x^4
+ 7x + 6x^4
------------------
x + 9x^4
Izzy is buying a car that costs $12,764. She must pay $2,000 the day she buys the car and then $299 every month until the car is paid off. How many months will it take for Izzy to pay for the car?
Answer:
Step-by-step explanation:
50
What is the value of 3.5 (11) + 1.9 (11) + 1.6 (11)?What is the value of 20 + 3 (7 + 4) + 5 + 2 (7 + 9)?
Answer:
1)77 2)90
Step-by-step explanation:
1)take 11 common
therefore, 11(3.5+1.9+1.6)
=11(7)
=77 (multiply 11 with 7)
2)First solve the numbers in bracket
20 +( 3×11 )+ 5 +( 2×16)
=20+33+5+32
=90
Vincent earns $546 on Monday and he earns $352 on Tuesday. How much total money does Vincent earn?
Answer:
$898
Step-by-step explanation:
Easy, 546 + 352 =
898
solve for θ. sinθ = cos(θ+10)
a. 6°
b.66°
c.84°
d.40°
Answer: d. 40°
Step-by-step explanation:
Use the Cofunction Identity: sin Ф = cos (90° - Ф)
sin Ф = cos (Ф + 10) = cos (90° - Ф)
⇒ Ф + 10 = 90 - Ф
2Ф + 10 = 90
2Ф = 80
Ф = 40
The perimeter of a rectangle is 42 cm. The width is 7 cm less than the length.
Answer:
Length = 14Width =7Step-by-step explanation:
[tex]Let \:the\:length\:be \:x\\Perimeter = 42 cm\\Width = x -7\\\\P = 2(l+b)\\\\42 = 2(x+(x-7))\\\\42 = 2(x +x-7)\\42 = 2(2x-7)\\42 = 4x -14\\Collect\:like\:terms\\\\42+14=4x\\56 = 4x\\\\Divide \:both\:sides\:of\:the\:equation\:by \:4\\\frac{56}{4} = \frac{4x}{4} \\\\14 =x\\Length = 14\\Width = x-7\\Width = 14-7\\\\Width = 7[/tex]
You own 24 CDs. You want to randomly arrange 7 of them in a CD rack. What is the probability that the rack ends up in alphabetical order
Answer:
the probability that the rack ends up in alphabetical order is 0.0001984
Step-by-step explanation:
Given that:
You own 24 CDs. You want to randomly arrange 7 of them in a CD rack.
Th probability that the rack ends up in alphabetical order can be determined by taking note of the permutations and combinations.
From above; all possible permutations of size 7 we can derive from 24 is
24P7
Similarly,we are meant to estimate all the possible ways a unique set of 7 things can be gotten from a total of 24
i.e
24 C7
∴
The probability = [tex]\dfrac{^{24}{C}_7}{^{24}{P}_7}[/tex]
= [tex]\dfrac{\dfrac{24!}{7!(24-7)!} }{ \dfrac{24!}{(24-7)!} }[/tex]
=[tex]\dfrac{\dfrac{24!}{7!(17)!} }{ \dfrac{24!}{(17)!} }[/tex]
= [tex]\dfrac{346104}{ 1.74436416 \times 10^9}[/tex]
= 0.0001984
the probability that the rack ends up in alphabetical order is 0.0001984
The probability that the rack ends up in alphabetical order is 0.0001984
The total number of CD is given as:
[tex]\mathbf{n = 24}[/tex]
The number of CDs to select is given as:
[tex]\mathbf{r = 7}[/tex]
The number of arrangement of 7CDs in 24 is represented as 24P7
So, we have:
[tex]\mathbf{^{24}P_7 = \frac{24!}{(24 - 7)!}}[/tex]
[tex]\mathbf{^{24}P_7 = \frac{24!}{17!}}[/tex]
Simplify
[tex]\mathbf{^{24}P_7 =1744364160}[/tex]
The number of selecting 7 CDs from 24 is represented as 24C7
So, we have:
[tex]\mathbf{^{24}C_7 = \frac{24!}{(24 - 7)!7!}}[/tex]
[tex]\mathbf{^{24}C_7 = \frac{24!}{17!!7}}[/tex]
Simplify
[tex]\mathbf{^{24}C_7 =346104}[/tex]
So, the probability is:
[tex]\mathbf{Pr = \frac{346104}{1744364160}}[/tex]
Divide
[tex]\mathbf{Pr = 0.0001984}[/tex]
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A distribution is negatively skewed. Which is the most probable order for the three measures of central tendency
Options :
a mean - 40, median - 50, mode - 60
b. mean-60, median - 50, mode - 40
c. mean - 40, median-60, mode - 50
d. mean - 50, median - 50, mode - 50
Answer: mean - 40, median - 50, mode - 60
Step-by-step explanation: A negatively skewed distribution is characterized by it long tail being positioned to the left(negative direction) with its peak positioned to the right (positive direction) of the distribution. On a general note, the mean is always positioned towards the left or negative side if the peak, with the median coming next and usually positioned to the right of the mean and the mode positioned to the right side of the median.
Hence, for a negatively skewed distribution, the mean has the least value followed by the median, with the mode boasting the highest.
That is : mean < median < mode
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Answer: 45 1/2
Step-by-step explanation:
Volume = 3 1/2 x 4 x 3 1/4
= 91/2
= 45 1/2 or 45.5
Answer:
45. 1/2 cubic inches
Step-by-step explanation:
Since volume of a cube = length x width x height, or V=Bh, we need to multiply 3 1/2, 4, and 3 1/4 together. 3.5 (3 1/2) x 4 = 14. 14 x 3.25 (3 1/4) is 45.5. This is also 45 1/2 in fraction form.
(60b ÷ 5) + c when b= 1/2 and c= 11
Answer:
17
Step-by-step explanation:
(60b divided by 5) + c
(60(1/2) divided by 5) + 11
(30 divided by 5) + 11
6 + 11
17
the table represents a function what is f(5)?
Answer:
U should delete the q btw
Use 5 as the value of x
Step-by-step explanation:
Answer: it’s A. -8
Step-by-step explanation: just took the test on edge
g The false positive rate, P(+|N), for a test is given as 0.04. What is the specificity for this test?
Answer:
Step-by-step explanation:
Let us consider a data of prevalent diseases.
If the false positive rate is P(Test + | N) = 0.04
Therefore, sensitivity is defined as the probability of a positive test result given the presence of the disease. This can be written as: P (positive test | disease present).
Specificity is defined as the probability of a negative test result given absence of disease, that is, P (negativetest | diseaseabsent). PPV is defined as the probability of the presence of disease given a positive test result, ie, P (disease present | positivetest).