The solution of the inequality is x < 5
How to determine the solution to the inequalityInequalities are defined as unequal comparison between two expressions, numbers or equations on the basis of their sizes on the number line.
From the information given, we have that;
-8<4(8-2x)
expand the bracket
-8 < 32 - 8x
collect like terms
-8 - 32 < -8x
subtract the like terms
-40 < - 8x
Make 'x' the subject of formula, we have to divide both sides by the coefficient of x, we get;
-40/-8 < -8x/-8
Divide the values
x < 5
Hence, the value is x < 5
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A child's toy is in the shape of a square pyramid. The pyramid stands 20 inches tall and each side of the base measures 24 inches.
Half of the surface area of the pyramid is black and the remainder is yellow.
What is the surface area of the toy that is yellow?
Enter your answer, rounded to the nearest tenth, in the box.
The surface area of the toy that is yellow is 847.8 inches², to the nearest tenth.
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object.
A square pyramid is a three dimensional object with one square base and 4 four triangular lateral faces.
Total surface area of the pyramid = Area of the base + 4(area of triangular face)
Base length = 24 inches
Base area = 24² = 576 inches²
Height of the pyramid = 20 inches
The slant height, l of the triangle can be found as,
l = [tex]\sqrt{(\frac{a}{2} )^2+h^2}[/tex], where a is the length of the base and h is the height.
l = [tex]\sqrt{12^2+20^2}[/tex]
= √544
= √(34 × 16)
= 4√34 inches
Area of 4 triangular faces = 4 ([tex]\frac{1}{2}[/tex] × 24 × 4√34)
= 2 × 24 × 4√34
= 192√34 inches²
Total surface area = 192√34 inches² + 576 inches²
= (192√34 + 576) inches²
= 1695.5428 inches²
Surface area of toy that is yellow = 1695.5 / 2 = 847.8 inches², to the nearest tenth.
Hence the surface area of the yellow part of toy is 847.8 inches², to the nearest tenth.
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when random assignment fails to create equivalent groups, the problem of occurs. a. external validity b. sampling error c. self-selection d. third variables
Answer:
Step-by-step explanation: A, B, C, and D because any of those 4 options can occur.7. (2 points) how many distinct 10-letter arrangements can be formed from the letters in the word statistics?
The number of distinct 10-letter arrangements that can be formed from the letters in the word "statistics" is 40320, which can be calculated by finding the permutation of 8 objects taken 8 at a time
Permutation is a mathematical concept that deals with counting the number of ways to arrange a set of objects in a particular order.
The number of permutations of a set of n objects taken r at a time can be calculated using the formula:
=> n! / (n - r)!.
Where "n!" represents n factorial, which is the product of all positive integers less than or equal to n.
In this case, we are going to find out the number of distinct 10-letter arrangements that can be formed from the letters in the word "statistics".
In our case, the number of objects is 8 (the letters in the word "statistics") and we are taking 10 at a time, so the formula becomes:
=> 8! / (8 - 10)! = 8! / (-2)!.
The factorial of a negative number is undefined, so this case is not possible.
Since we cannot take more objects than the number of available objects, we have to find the number of permutations of 8 objects taken 8 at a time. The formula becomes:
=> 8! / (8 - 8)! = 8! / 0! = 8!.
Finally, 8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40320,
which means that there are 40320 distinct 10-letter arrangements that can be formed from the letters in the word "statistics".
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11 increased by twice groans hight
Answer:
Step-by-step explanation:
The expression "11 increased by twice Grogan's height" can be written as:
11 + 2Grogan's height
For example, if Grogan's height is 5 feet, the expression would be:
11 + 2(5) = 11 + 10 = 21
NEED HELP!!! ill give brain points. Explain or show why Priya's conclusion is incorrect.
pls answer the following question circled in red
this question is asking how to compare linear functions (algebra 1)
Answer:
yes Priya's conclusion is incorrect
Step-by-step explanation:
x square will always be greater than the actual value of x
but in this expression
f (x ) = 10 * x²
g (x) = 3 * 2raise to the power x
priya's conclusion is incorrect because in the other expression the power of x is increasing exponentially so eventually g(x) will be greater than f(x)
as for x = 10
f(x) = 10 * 10² = 1000
g(x) = 3 * 2raise to power 10 = 3 * 1024 = 3072
what is the answer? i need help
The area of the lateral surfaces will be 192.55 square centimetres.
What is an area of a prism?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the prism in a two-dimensional plane is called as the area of the prism.
Given that there is a triangular prism having sides the height of the triangular side is 4.3 cm and its base is 5 cm.
The lateral surface area will be calculated as:-
SA = 2 x ( 5 x W ) + 10 x 50 + ( 1 / 2 ) x 5 x 4.3
W = √ ( 5² + 4.3²)
W = √43.49
W = 6.59 cm
SA = 2 x ( 10 x W ) + 10 x 50 + ( 1 / 2 ) x 5 x 4.3
SA = 2 x ( 10 x 6.59 ) + 10 x 5 + ( 1 / 2 ) x 5 x 4.3
SA = 131.8 + 50 + 10.75
SA = 192.55 square centimetres
Therefore, the area of the prism will be 192.55 square centimetres.
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Select strong association moderate assossiation or weak association for each correlation 0.8, .25 ,0.9, 0.65coeffcient
A correlation coefficient of 0.8 or higher indicates a strong association between two variables, while a coefficient between 0.5 and 0.7 indicates a moderate association and a coefficient of 0.4 or lower indicates a weak association.
0.8 - Strong Association
0.25 - Weak Association
0.9 - Strong Association
0.65 - Moderate Association
The strength of a correlation is determined by its correlation coefficient. A correlation coefficient of 0.8 or higher is considered strong, a correlation coefficient between 0.5 and 0.7 is considered moderate, and a correlation coefficient of 0.4 or lower is considered weak. A correlation coefficient of 0.8 indicates a strong association between two variables, a correlation coefficient of 0.25 indicates a weak association, a correlation coefficient of 0.9 indicates a strong association, and a correlation coefficient of 0.65 indicates a moderate association.
A correlation coefficient of 0.8 or higher indicates a strong association between two variables, while a coefficient between 0.5 and 0.7 indicates a moderate association and a coefficient of 0.4 or lower indicates a weak association. For the given correlation coefficients, 0.8 and 0.9 indicate strong associations, 0.25 indicates a weak association, and 0.65 indicates a moderate association.
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1. "the sum of 16 and x"
Answer:
16+X is the answer because 16 has no variable beside it X is also standing on it's own so they can't even group like terms
Answer:
Step-by-step explanation:
Date
Period
RP6
Proportions and Scale Factor Mastery Review
1. A science textbook uses a scale of 4 cm =3 mm for the drawings of small insects. What is the
actual length of a dragonfly if the drawing is 8.5 cm?
The actual length of the dragonfly if the drawing is 8. 5 cm, can be found to be 6. 375 mm
How to find the actual length ?The scale on the science textbook is such that every 4 cm of the drawing of an insect is the same as 3 mm of the actual insect.
If a drawing is 8. 5 cm therefore, the actual length of the dragonfly would be :
= ( Drawing length of dragonfly x Scale of insect ) / Drawing scale of insect
The actual length is therefore :
= ( 8. 5 x 3 ) / 4
= 6. 375 mm
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Leah is making a square wooden picture frame for woodworking class. After dividing a piece of wood she wants to use into 4 equal pieces, Leah figures each side of her frame can be at most 12 inches long. Let x represent the perimeter of the picture frame. Which inequality describes the problem?
Therefore , the solution of the given problem of inequality comes out to be x ≤ 48.
What does inequality imply in reality?A relationship or collection of numbers without the equal sign is known as a mathematical inequality. Equilibrium is typically followed by equity. Inequality happens when two factors are not equal. Differences exist between variable equity and inequality. Because the digits are not identical or similar, the most typical symbol was selected (). Any difference, regardless of how small or large, can be used to evaluate values.
Here,
If each side of the frame can be at most 12 inches long, then the perimeter of the frame can be at most 4 x 12 = 48 inches.
So, the inequality that describes the problem is:
x ≤ 48.
Therefore , the solution of the given problem of inequality comes out to be x ≤ 48.
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the probability that a doctor correctly diagnoses a particular illness is 0.7. given that the doctor makes an incorrect diagnosis, the probability that the patient files a lawsuit is 0.9. what is the probability that the doctor makes an incorrect diagnosis and the patient sues?
The probability that the doctor makes an incorrect diagnosis and the patient sues is 0.27.
The probability that a doctor correctly diagnoses a particular illness is 0.7.
P(A) = 0.7
Therefore, the probability that a doctor incorrectly diagnose illness is,
P(A)' = 1-0.7 = 0.3
IF the doctor made a incorrect diagnosis, the probability that the patient files a lawsuit is 0.9.
P(B) = 0.9
The probability of doctor makes an incorrect diagnosis and the patient sues,
P(C) = 0.3 * 0.9 = 0.27
The probability that the doctor makes an incorrect diagnosis and the patient sues is 0.27.
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PLS ANSWER ONLY IF YOU KNOW THE RIGHT ANSWER
30 POINTS
Answer:
y = -17
Step-by-step explanation:
None
pls help im struggling
find the change in the temperature during the 1.5-hour period after the storm began. round to 3 decimal places.
This value can be rounded to 3 decimal places, which would be 3.800°F.
What is value?Values relative what made it up importance of something if can refer to an intangible concepts such as person principle of it tangible objects such as rare coin value where body widely across culture society and individual can even vary within the same individual over time.
To find the change in temperature during a 1.5-hour period after a storm began, it would be necessary to take two temperature readings, one before the storm began and one after the storm ended. By subtracting the two readings, the change in temperature can be determined. For example, if the temperature before the storm began was 75.4°F and the temperature after the storm ended was 79.2°F, the change in temperature would be 3.8°F. This value can be rounded to 3 decimal places, which would be 3.800°F.
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A teacher tells 36 students to form 4 equal groups. Write and solve a
equation to find how many students s there should be in
multiplication
each group.
ehomego avai
4.32
Answer:
Step-by-step explanation:
36 divided by 4 is 9, so the answer would be 9
3 divided by 4
who ever answers 1st will get 100 pts sent to them
Answer: 0.75
Step-by-step explanation:
30/15 + 25/40 + 30/35 =
Answer:
735/420 + 2 = 735/420 + 420/420 = 1155/420
Step-by-step explanation:
To add the three fractions, we need to find a common denominator. A common denominator for all three fractions is 420:
30/15 = 2
25/40 = 25/40 * 3/3 = 75/120
30/35 = 30/35 * 12/12 = 360/420
Adding the three fractions with the common denominator:
2 + 75/120 + 360/420 = 2 + 375/420 + 360/420
Combining like terms:
2 + 735/420 = 2 + 735/420
The answer is 735/420 + 2 = 735/420 + 420/420 = 1155/420.
nails cost $12.99 per box, and screws cost $14.99 per box. a carpenter must buy both nails and screws and can spend no more than $60. which system of inequalities represents this situation, where n represents the number of boxes of nails and s represents the number of boxes of screws?
The cost of nails can be represented as 12.99n, and the cost of screws can be represented as 14.99s.
The cost of buying nails and screws can be represented by a system of inequalities where "n" represents the number of boxes of nails and "s" represents the number of boxes of screws.
The cost of one box of nails is $12.99 and the cost of one box of screws is $14.99. Hence, the cost of "n" boxes of nails is represented by 12.99n and the cost of "s" boxes of screws is represented by 14.99s. The carpenter has a budget of $60 and can spend no more than that.
Therefore, the combined cost of buying nails and screws must be less than or equal to $60. This requirement can be represented by the inequality 12.99n + 14.99s <= 60.
To make the calculation easier, we can also express the inequality as n + s <= 4.62, where 4.62 is obtained by dividing $60 by $12.99. This system of inequalities represents the carpenter's budget constraint and helps to determine the number of boxes of nails and screws that can be purchased within the budget.
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find n and s. n=blank, s=blank
The sides n and s of the given similar triangles are 12 and 10 respectively.
What are similar triangles?
If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are similar. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.
The polygon with three sides is a triangle. The prerequisites for a triangle's similarity are that the corresponding angles on both triangles must be equal, and the corresponding sides must be proportional to one another.
In the given figure both triangles are similar triangles.
So according to the properties of similar triangles,
[tex]\frac{15}{s} = \frac{9}{6}=\frac{n}{8}[/tex]
Solving the above equations,
15/s = 9/6
s = 10
n/8 = 9/6
n = 12
Therefore the sides n and s of the given similar triangles are 12 and 10 respectively.
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What is the shape triangle measure of angle B?
A
80°
B
8x+2
C
6x
For the triangle ABC the interior angles measures ∠A = 80°, ∠B = 58°, and ∠C = 42°.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
According to the angles of a triangle theorem, the sum of angles of a triangle is 180°.
The measure of ∠A = 80°.
The measure of ∠B = 8x + 2.
The measure of ∠C = 6x.
The equation is -
∠A + ∠B + ∠C = 180°
Substitute the values into the equation -
80° + 8x + 2 + 6x = 180
Collect the like terms -
8x + 6x = 180 - 80 - 2
14x = 98
x = 98/14
x = 7°
So, the measure of ∠B = 8(7) + 2 = 58°
The measure of ∠C = 6(7) = 42°
The interior angles of the triangle are 80°, 58° and 42°.
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what is the smallest number you can make from: 5,2,4,3
Match each quotient with its answer when expressed in the form of a + bi
Match each quotient of the complex numbers accordingly as shown below.
How to match each quotient when expressed in the form of a + bi?
A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1. The real part of a complex number is represented by a, while the imaginary part is represented by bi.
No. 1
Multiply the numerator and denominator by 3-4i:
1/(3 + 4i) = 1/(3 + 4i) * (3 - 4i)/(3 - 4i)
= (3 - 4i)/(9 + 16)
= (3 - 4i)/25
= 3/25 - 4/25 i
No. 2
Multiply the numerator and denominator by 3+4i:
1/(3 - 4i) = 1/(3 - 4i) * (3 + 4i)/(3 + 4i)
= (3 + 4i)/(9 + 16)
= (3 + 4i)/25
= 3/25 + 4/25 i
No. 3
i/i = 1
= 1 + 0i
No. 4
Multiply the numerator and denominator by 3-4i:
(3 - 4i)/(3 + 4i) = (3 - 4i)/(3 + 4i) * (3 - 4i)/(3 - 4i)
= (9 - 24i -16) / (9 + 16)
= (-7 - 24i) / 25
= -7/25 - 24i/25
No. 5
(3 - 4i)/ 1 = 3 - 4i
No. 6
Multiply the numerator and denominator by 3+4i:
(3 + 4i)/(3 - 4i) = (3 + 4i)/(3 - 4i) * (3 + 4i)/(3 + 4i)
= (9 + 24i -16) / (9 + 16)
= (-7 + 24i) / 25
= -7/25 + 24i/25
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3p + –7.81 = –13.81 solve for p
Step-by-step explanation:
3p + (-)7.81 = -13.81
3p = -13.81 + 7.81
3p = -6
p = -6/3
p = -2
What is 1 1/2 close to
The given mixed fraction can be written in decimal form as 1.5.
What are mixed fractions?These are just improper fractions written as a sum of whole number and a proper fraction. (improper fraction has the upper value(also called numerator) bigger or equal to denominator(the bottom value) and proper fraction has numerator value is less than that of the denominator)
The given mixed fraction is [tex]1\frac{1}{2}[/tex].
Now, the given mixed fraction can be written as 3/2
3/2 can be written in decimal number as 1.5.
Decimal number 1.5 is between 1 and 2.
Therefore, the given mixed fraction can be written in decimal form as 1.5.
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OMG PLS HELP ME 100 points will GIVE BRAINLIEST
Express sin
�
S as a fraction in simplest terms.
Answer:
Step-by-step explanation:
I gotchu.
sinS = 2/9
S = sin^-1(2/9)
S = 12.84 = 321/25 or 12 21/25
Binary calculation 1101 x 101 +100
Step-by-step explanation:
=01000101
is the answer
The binary value of the given expression is 111101.
To multiply binary numbers, we use the same process as with decimal numbers, but using only 0s and 1s. We can use the distributive property of multiplication to break down the problem into simpler multiplication and addition operations.
First, we multiply 1101 by 101:
1101
x 101
-----
1101
1101
------
111001
Next, we add 100 to the result:
111001
+ 100
-------
111101
The decimal value of 111101 is given by,
(111101)₂ = (61)₁₀
Therefore, the product of 1101 and 101, plus 100, is 111101 in binary.
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What percent of 112 is 21?
21 is 18.75% of 112. Percentage is widely used to represent a difference or contrast between two numbers.
What do you mean by percentage?A percentage is a way to express a number as a fraction of 100. It is often used to express a change or a comparison between two numbers. The symbol for percentage is %, and it represents the fraction of 100. For example, 50% means 50 out of 100, or 1/2.
Percentages are often used to represent increases or decreases in a quantity, as well as ratios and proportions. For example, if the price of a product increases by 20%, it means the new price is 120% of the original price, or 1.2 times the original price. If a student scores 80% on a test, it means they answered 80 out of 100 questions correctly.
Percentages can be easily converted to decimals or fractions by dividing by 100. For example, 50% can be written as 0.5 as a decimal or 1/2 as a fraction. Similarly, 75% can be written as 0.75 as a decimal or 3/4 as a fraction.
To find what percent 21 is of 112, we can use the formula:
Percent = (Part ÷ Whole) x 100
In this case, the part is 21 and the whole is 112, so:
Percent = (21 ÷ 112) x 100
Percent = 0.1875 x 100
Percent = 18.75
Therefore, 21 is 18.75% of 112.
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Enter a negative number that have a value greater then 8
A negative number that have a value greater then 8 does not exist
How to determine the negative valueFrom the question, we have the following parameters that can be used in our computation:
negative number that have a value greater then 8
The number 8 is a positive number
As a general rule:
No negative number is greater than a positive number
Hence, the negative number does not exist (DNE)
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An art class is painting a rectangular mural on their classroom wall . The mural will be composed of large square blocks that are 8 in. long and 16 in. high. The mural is 12 in. high. What is its length?
Part A: The outside border of each square block is covered with the blue paint. How many square inches of each block are covered by blue paint?. Part B: The entire mural will have 25 identical blocks. How many square inches of the entire mural will be covered by white paint?
Part A: Each block will have an area of 128 square inches (8 in. x 16 in.), but the outside border of each block will be covered with blue paint.
What is area?Area is the measurement of the space contained within a two-dimensional surface.
The outside border of each block is 8 in. long and 16 in. high, for a total of 128 square inches of each block that is covered in blue paint.
Part B: The entire mural will have 25 identical blocks, so the total number of square inches of the entire mural that will be covered by white paint is 3,200 square inches (25 blocks x 128 square inches per block).
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records show that 10% of all college students are foreign students who also smoke. it is also known that 40% of all foreign college students smoke. what percent of the students at this university are foreign?
The percentage of the students at the university which are foreign are 25% by conditional probability formula.
According to the question, 10% of all college students are foreign students who also smoke and it is also known that 40% of all foreign college students smoke.
We use the conditional probability formula to solve this question.
Let foreign students be denoted as F
Let students smoking be denoted as S
We know that 10% of all college students are foreign students who also smoke this means
P(F ∩ S) = 0.1
and 40% of all foreign college students smoke which means
P(S/F) = 0.4
So, the percentage of the students at this university who are foreign can be calculated as
[tex]P(F) = \frac{0.1}{0.4}[/tex] = 0.25
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