The probability that a randomly chosen child has a height of less than 68.15 inches is 0.9162, the probability that a randomly chosen child has a height of more than 54.4 inches is 0.6255.
Simply put, probability is the liability that commodity will do. When we do not know how an event will turn out, we can bandy the liability or liability of several issues. Statistics is the study of events that follow a probability distribution.
a) We need to find p(x<68.15)
Standardize x to z, we have, z = (68.15-μ)/σ
=(68.15-57)/8.1
=1.38
Reading from standard normal tables,
p(z<1.38) =0.9162.
Therefore, the probability that a randomly chosen child has a height of less than 68.15 inches is 0.9162.
b) We need to find p(x>54.4)
Standardize x to z, we have, z = (54.4-μ)/σ
=(54.4-57)/8.1
=-0.32
Reading from standard normal tables,
p(z>-0.32) = 0.6255
Therefore, the probability that a randomly chosen child has a height of more than 54.4 inches is 0.6255.
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A Set of Speakers costs $35 and Songs cost $195 each. The sales tax
rate is 8.25%. The expression 0.0825(35+ 195s) can be used to determine
the amount of sales tax due on the entire purchase of a set of Speakers
and S.Songs. Expand the expression and round to the nearest hundredth.
The amount of sales tax due on the entire purchase of a set of speakers and s songs is given by expression 2.8875+16s
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given that :
Cost of speaker = $35
Cost per song = $195
Sales tax rate = 8.25%
Expression to obtain the amount of sales tax on entire purchase : 0.0825(35+ 195s)
Using distributive law to expand the expression :
0.0825(35+ 195s)
= 2.8875+16s
Hence, the amount of sales tax due on the entire purchase of a set of speakers and s songs is given by expression 2.8875+16s
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Which figures have equal area? Choose all that are correct.
Equivalence means to be same, whether it be value, temperature, size, etc.
Let's take a look at shape 1.
Shape 1 has a base of 3, and a height of 4, but there is a gap with a width of 1 and a height of 2. So, we can use this equation to figure out the area:
(3 × 4) - (1 × 2) = 10So, shape 1 has an area of 10 units.
Let's look at shape 2.
Shape 2 has a base of 2, and a height of 4, but there is also a gap, with a width of 1 and a height of 3. So, we can use this equation to figure out the area:
(2 × 4) - (1 × 3) = 5So, shape 2 has an area of 5 units.
Let's look at shape 3.
Shape 3 consists of 4 right triangles, put together to form an arrowhead. The shape has a base of 4, and a height of 2. So, we can use this equation to figure out the area:
(4 × 2) ÷ 2 = 4So, shape 3 has an area of 4 units.
Let's look at shape 4.
Shape 4 consists of 4 right triangles, put together to form a diamond. The shape has a base of 4, and a height of 2. So, we can use this equation to figure out the area:
(4 × 2) ÷ 2 = 4So, shape 4 has an area of 4 units.
Looking to the final shape (5), we can see it consists of a long rectangle and 2 right triangles. Instead of calculating the base and height of the entire shape, we can break it into pieces, making a rectangle that has a base of 3, and a height of 1. Then we are left a shape that has a base of 2, and a height of 3. So, we can use this equation to figure out the area:
(3 × 1) + ([2 × 3] ÷ 2) = 6So, shape 5 has an area of 6 units.
Let's compare the area of all of the shapes.
Has an area of 10 square units. Has an area of 5 square units. Has an area of 4 square units. Has an area of 4 square units. Has an area of 6 square units.Therefore, the two figures that have equal areas are shapes 3 and 4.
A soccer player has a large cylindrical water cooler that measures 3.5 feet in diameter and is 2 feet tall. If there are approximately 7.48 gallons of water in a cubic foot, how many gallons of water are in the water cooler when it is completely full? Use π = 3.14 and round to the nearest hundredth.
The volume of the water in the water cooler when it is completely full is 82.21 gallons.
What is a cylinder?
One of the most fundamental curvilinear geometric shapes, a cylinder has traditionally been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In many contemporary branches of geometry and topology, a cylinder can also be defined as an infinitely curvilinear surface.
Given that the height of a cylinder is 3.5 feet. The diameter of the cylinder is 2 feet.
The radius of the cylinder is half of the diameter.
The radius of the cylinder is 2/2 = 1 foot.
The volume of a cylinder is πr²h.
r = radius, h = height
The volume of the cylinder is
π×1²×3.5
= 3.14 × 3.5
= 10.99 cubic foot
= 10.99 × 7.48 gallons
= 82.205 gallons
= 82.21 gallons
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Question 1
Kylie and her family need to buy a new refrigerator. The space available for the refrigerator measures 37 in. wide, 72 in. high, and 24 in. deep.
Which size refrigerator would be the BEST fit for the available space?
70,000 in ³
000
A
B
C
69,936 in.³
53,900 in.3
D 42,000 in.³
Answer:
Answer is very unclear, but I think it is C.
Step-by-step explanation:
The best fit for the available space would most likely be 53,900 in.³
4. John and Mitchell are buying snack from the break cart at school. John bought 2 bags of chips and 3
candy bars for $8.50. Mitchell bought 4 bags of chips and 2 candy bars for $11. How much did each item
cost?
Define your variables. x =
Write a system of equations.
Solve using any method.
y=_
a group of 100 people contains 60 democrats and 35 republicans. if there are 60 women and 40 of the democrats are women, what is the probability that a person selected at random is a democrat or a woman?
The probability of selecting a person who is either a Democrat or a woman is 0.8, or 80%.
Probability is a branch of mathematics that deals with the study of random events. It is used to predict the likelihood of an event occurring.
Let's start by finding the probability of selecting a Democrat. We are given that there are 60 Democrats in the group of 100 people. Therefore, the probability of selecting a Democrat at random is:
P(Democrat) = 60/100 = 0.6
Next, let's find the probability of selecting a woman. We are given that there are 60 women in the group of 100 people. Therefore, the probability of selecting a woman at random is:
P(Woman) = 60/100 = 0.6
Now, we need to find the probability of selecting both a Democrat and a woman. We are given that 40 of the Democrats are women. Therefore, the probability of selecting a woman who is also a Democrat is:
P(Democrat and Woman) = 40/100 = 0.4
To find the probability of selecting a person who is either a Democrat or a woman, we add the probabilities of selecting a Democrat and selecting a woman, and then subtract the probability of selecting both a Democrat and a woman. Therefore, the probability of selecting a person who is either a Democrat or a woman is:
P(Democrat or Woman) = P(Democrat) + P(Woman) - P(Democrat and Woman)
= 0.6 + 0.6 - 0.4
= 0.8
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please help me i dont understand this
Answer: 57
Step-by-step explanation: I recommend learning angle properties, pictures on the internet might help ya out
Clear my choice
Which expression is equivalent to
(-√8 -√2) + √-36
The expression equivalent to (-√8 -√2) + √-36 is -3√2 + 6i.
What are complex numbers?A real number and an imaginary number are effectively combined to create a complex number. The complex number is written as a+ib, where a and ib are real and imaginary numbers, respectively. Additionally, I = -1 and both a and b are real numbers.
Consequently, a complex number is a straightforward illustration of the addition of two integers, specifically a real number and an imaginary number. It consists of two parts: one that is entirely real, the other entirely fantastical.
The given expression is:
(-√8 -√2) + √-36
The expression can be written as:
(-2√2 - √2) + √(i)²(6)²
Taking the common term:
√2(-2 - 1) + 6i
Simplifying the expression:
-3√2 + 6i
Hence, the expression equivalent to (-√8 -√2) + √-36 is -3√2 + 6i.
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solve for angle BD only
Answer: BD = 60.34
Step-by-step explanation:
8x -33 = 2x+37
Take away 2x from both sides ( the 2x will cancel out)
= 6x - 33= 37
Add the 33 to both sides. (The -33 will cancel out)
Now you are left with 6x = 70
Divide both sides by 6.
x = 11.67 (rounded by the hundredth) (11.66666...)
Now to figure out BD your new equation is 2(11.67) + 37
After multiplying you get 23.34 + 37.
BD = 60.34
Hope this helps. This is the way I learned.
find the following arc measures
Answer:
m angleJ= 53, m angle JML = 63.5
Step-by-step explanation:
As this is a circle, KJ and KL are radii, which are equal
If we join J and L to form JL, Triangle KJL becomes and isosceles triangle( two sides equal).
That means, the angles J and L are equal (isosceles triangle thm).
Therefore- m angleJ = 180 - 127
m angleJ = 53
Join J and K, and L and K
Another circle theorem- The angle subtended by an arc/chord on the centre is double the angle subtended by the chord on any other point on the circle.
Therefore- angle JML = (1/2)127
So, m angleJML = 63.5
to find m∠JML, you can stop when you get the step 3x=126 degrees, right?
No, you cannot stop at the step 3x = 126 degrees. The measure of angle JML is approximately 56.67 degrees
What is the measure of angle θ?
A radian is the length of an arc formed by an angle that, when shown as a central angle, equals the length of the circle's radius.
No, you cannot stop at the step 3x = 126 degrees.
To find the measure of angle JML, we need to solve for x and then use that value to find the measure of the angle.
We can start by using the fact that the angles in triangle JLM must add up to 180 degrees. We have:
m∠JLM + m∠JML + m∠LMJ = 180
Substituting the given values, we get:
4x + (2x + 18) + (3x - 12) = 180
Simplifying and combining like terms, we get:
9x + 6 = 180
Subtracting 6 from both sides, we get:
9x = 174
Dividing both sides by 9, we get:
x = 19.33...
Now that we have the value of x, we can use it to find the measure of angle JML. We have:
m∠JML = 2x + 18
Substituting x = 19.33..., we get:
m∠JML = 2(19.33...) + 18 = 56.67...
Therefore, the measure of ∠JML is approximately 56.67 degrees
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pleaseeee helppppp :(
jake and kim share some money in the ratio 1:3
kim gets $90 more than jake.
how much does kim get
Answer: $135
Step-by-step explanation:
We have the ratio 1 : 3.
Kim gets $90 more than Jake.
So 1 : 3 can also be written as x : x+90
If x * 3 equals x+90, we can create the equation 3x=x+90. Solving this results in x being equal to 45
Kim gets $135 (x+90=45+90=135)
in a class of 26 students,15 of them like maths,13 of them like english and 9 doesnt like eitherwhats the probability that a student choosen at random likes english but not maths
The probability that a student choosen at random likes english but not maths is 299/676.
Let A be the event that a student likes math, and B be the event that a student likes English.
From the given information, we know that:
P(A) = 15/26
P(B) = 13/26
P(neither A nor B) = 9/26
To find the probability that a student chosen at random likes English but not math, we can use the formula:
P(B and not A) = P(B) - P(A and B)
The probability of A and B can be found by multiplying the probabilities of A and B together, since they are not independent:
P(A and B) = P(A) × P(B) = (15/26) × (13/26) = 195/676
Substituting the given probabilities into the formula, we get:
P(B and not A) = (13/26) - (195/676)
Simplifying, we get:
P(B and not A) = 299/676
Therefore, the probability that a student chosen at random likes English but not math is 299/676.
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C) If a person needs 103. 8 ml of water from burning C₁2H24O12. How many grams
of C12H24012 is needed to acquire the needed volume of water? (hint: what is the
density of water?)
The density of water is 1 g/mL, so for this problem, we would multiply 103.8 mL by 1 g/mL to get our answer of 103.8 grams.
The density of water is 1 gram per milliliter (1 g/mL). This means that for every milliliter of water, there is 1 gram. Therefore, to answer the question of how many grams of C12H24012 is needed to acquire the needed volume of water (103.8 mL), we need to multiply the volume of water by the density of water. To do this, we will use the equation: Mass (g) = Volume (mL) x Density (g/mL). For this problem, the equation would be: Mass (g) = 103.8 mL x 1 g/mL.Therefore, the answer to the question is 103.8 grams of C12H24012 is needed to acquire the needed volume of water.In conclusion, to figure out how many grams of C12H24012 is needed to acquire the needed volume of water, we need to multiply the volume of water (in mL) by the density of water (in g/mL). The density of water is 1 g/mL, so for this problem, we would multiply 103.8 mL by 1 g/mL to get our answer of 103.8 grams.
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susan hypothesizes that the students of a private school will score higher than the general population. susan records a sample mean equal to 578 and states the hypothesis as vs . select the best description for this type of test. a.) lower-tailed test b.) left-tailed test c.) two-tailed test d.) right-tailed test
Susan predicts that private school pupils will perform better than the general populace. The best description for this type of test is a right-tailed test.
In this scenario, Susan is testing the hypothesis that the mean score of the students of the private school is greater than 572, which is the mean score of the general population. This type of test, where the alternative hypothesis is "greater than" a specified value, is known as a right-tailed test or a one-tailed test (since the test is only considering one direction of deviation from the null hypothesis).
So the correct answer is d) a right-tailed test or a one-tailed test.
The complete question is:-
Susan hypothesizes that the students of a private school will score higher than the general population. Susan records a sample mean equal to 578 and states the hypothesis as μ= 572 vs μ>572. Select the best description for this type of test. a.) lower-tailed test b.) left-tailed test c.) two-tailed test d.) right-tailed test.
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Solve [tex]x^{2} -24=10x[/tex]
3/5 divided by 4/7 id ont get this can so,eome help
The expression which is equivalent to the given expression 3/5 divided by 4/7 is given by option d. 3/5 multiply 7/4.
The expression which is equivalent to the expression 3/5 divided by 4/7 is:
3/5 divided by 4/7 can be expressed as
= ( 3 / 5 ) ÷ ( 4 / 7 )
Convert division sign into multiplication sign we get,
= ( 3 / 5 ) × [ 1 / ( 4 / 7 ) ]
= ( 3 / 5 ) × ( 7 / 4 )
= 3/5 multiply 7/4
Therefore, the correct way of representing the expression 3/5 divided by 4/7 is equivalent to option d. 3/5 multiply 7/4.
The above question is incomplete, the complete question is:
Which of these expression is the same as 3/5 divided by 4/7?
a 3/5 divided 7/4
b 4/7 divided 3/5
c 3/5 multiply 4/7
d 3/5 multiply 7/4
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Subtract. Write the answer in standard form.
(13 + 9i) - (1-11) ?
Answer:
[tex]10^{1}[/tex]
Step-by-step explanation:
13 + 9 - 1 - 11
Add 13 and 9 to get 22.
22 - 1 - 11
Subtract 1 from 22 to get 21.
21 - 11
Subtract 11 from 21 to get 10.
10
prove, that 32^5-16^5+2^19 is divisible by 63 help asap
ill award brainlist
Step-by-step explanation:
Use PEMDAS (Order of operations).
Simplify exponents
33554432 - 1048576 + 54288
Add and subtract (left to right)
33030144
63 goes into 33030144 524288 times.
Answer:
2^19(63)
Step-by-step explanation:
(2^5)^5-(2^4)^5+2^19
2^25-2^20+2^19
2^19(2^6-2+1)
2^19(64-2+1)
2^19(63)
Find tn Will mark branliest!
The sequence is an arithmetic sequence
The equation of tn is Tn = -k^2 - k + 1 + (n - 1) * (k^2 + 2k + 3)
How to determine the equation of the functionFrom the question, we have the following parameters that can be used in our computation:
-k^2 - k + 1, k + 2, k^2 + 3k + 3, 2k^2 + 5k + 4
The above sequence is an arithmetic sequence
And the common difference (d) is
d = k + 2 + k^2 + k + 1
d = k^2 + 2k + 3
The nth term is then calculated as
Tn = a + (n - 1)d
So, we have
Tn = -k^2 - k + 1 + (n - 1) * (k^2 + 2k + 3)
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(PLEASE HELP ME ASAP THIS IS DUE TODAY)
An image of a parallelogram is shown.
A parallelogram with a base of 22 and one-half feet and a height of 19 and one-fourth feet.
What is the area of the parallelogram?
423 1/2 ft
427 1/2 ft
433 1/8 ft
455 1/8 ft
Answer:
433 1/8ft
Step-by-step explanation:
this is my answer
Use synthetic division to find the result when 4x^4-7x^3+7x^2-12x+15 is divided by x-1. If there is a remainder, express the result in the form q(x)+r(x)/b(x)
When given expression (4x⁴-7x³+7x²-12x+15)/(x-1) is solved, result in the form q(x)+r(x)/b(x) will be -7x² + 4 + 19/(x-1).
What precisely are expressions?Expressions in mathematics are mathematical statements that are made up of at least two sentences that contain numbers, variables, or both, and are connected by an operator. Addition, subtraction, multiplication, and division are examples of mathematical operations. For example, x + y is an equation that separates the terms x and y by an addition operator. There are two sorts of expressions in mathematics: numerical expressions, which include simply numbers, and algebraic expressions, which contain both numbers and variables.
e.g. A number is 6 times larger than another number, x. This statement may be expressed mathematically as x/2 + 6. Complex issues are solved using mathematical expressions.
Now,
Given expression to solve is (4x⁴-7x³+7x²-12x+15)/(x-1)
then dividing this
=4x⁴/x-1-7x³/x-1+7x²/x-1-12x/x-1+15/x-1
=4x³-3x²+4x-8+7/x-1 in form of q(x)+r(x)/b(x)
= 4x⁴/x-1-7x³/x-1+7x²/x-1-12x/x-1+15/x-1
= -7x² + 4 + 19/(x-1)
hence,
When given expression (4x⁴-7x³+7x²-12x+15)/(x-1) is solved, result in the form q(x)+r(x)/b(x) will be -7x² + 4 + 19/(x-1).
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53. The cutting tool on a lathe moves 3/128 in. along the piece being turned for each revolution of work. The piece revolves at 45 revolutions per minute. How long will it take to turn a length of 9 9/64-in. Find in one operation?
Using the concept of rates, the machine will complete 9 9/64 inches in 8.67 minutes
How long will it take to turn a particular length
To determine how long it will take to turn a particular length of iron, we can calculate the rate at which it works and it must be in a definite proportion.
If the lathe moves 3/128 in one revolution.
And the machine completes 45 revolutions in 1 minutes, we can determine how many inches in moves in that minute.
3/128 in = 1 rev
x in = 45
45 * (3/128) = 45 revolutions = 1 minute
1.054 inches in 1 minute.
We can further use this to determine the time it takes to move 9 9/64 inches
1.054 inches = 1 minute
9 9/64 inches = x minute
cross multiply both sides and solve
x = 8.67 minutes
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brianna is driving on a long road trip. she created the graph below to represent the gallons of gas left in her tank. what does the x-intercept in the graph represent?
The x-axis represents the distance traveled (in miles).
Considering that the x-axis shows the distance travelled (in miles) and the y-axis represents the amount of gas left in the tank (in gallons), the x-intercept would represent the point at which Brianna's gas tank is empty, and she would need to refill her tank to continue traveling. In other words, the x-intercept is the distance Brianna can travel before running out of gas, assuming her car's fuel efficiency remains constant and she does not refill her tank.
Two key lines known as the x and y axes are the building blocks of a graph.
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sean gets an average of 20 calls during his 8 hour work day. what is the probability that sean will get at most 9 calls in a 4 hour portion of his work day? round the final answer to three decimal places.
The probability that Sean will get at most 9 calls in a 4 hour portion of his work day is 0.037.
The probability that Sean will get at most 9 calls in a 4 hour portion of his work day can be calculated by using the Poisson distribution formula. The formula is [tex]P(x)=e^-μ(μ^x/x!)[/tex].
In this case, μ = 20/4 = 5.
Therefore, [tex]P(x=9) = e^-5(5^9/9!) = 0.037[/tex]
Rounding the answer to three decimal places, the probability that Sean will get at most 9 calls in a 4 hour portion of his work day is 0.037.
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Assume that adults have IQ scores that are normally distributed with a mean of μ=100 and a standard deviation σ=20. Find the probability that a randomly selected adult has an IQ less than 140.
The probability that a randomly selected adult has an IQ less than 140 is 97.72%.
What is the standard deviation?
The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.
Given that the mean of adults' IQ is μ=100 and the standard deviation is σ=20.
The formula of z-score is z = (X - μ)/σ
Putting the value of μ = 100, σ=20, and X = 140:
z = (140 - 100)/20
z = 40/20
z = 2
From z table, we get the value of z is 0.9772 = 97.72%
P(X<140) = P(z = 2.0) = 97.72%
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2. Two observers are 600 ft apart on opposite sides of a flagpole. The angles of elevation from the
observers to the top of the pole are 19 and 21°. Find the height of the flagpole. Round to the nearest
foot.
After finding the sides of the triangle using sine law, we found that the height of the flagpole is found to be 110.89 ft.
What is meant by sine law?
The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.
The side or unknown angle of an oblique triangle is found using the law of sine. Any triangle that is not a right triangle is referred to as an oblique triangle. At least two angles and their corresponding side measurements should be used at once for the sine law to function.
Given,
The distance between two observers = 600 ft
The angle of elevation of the first observer = 19°
The angle of elevation of the second observer = 21°
We are asked to find the height of the flagpole.
The figure is given below.
There are 2 right triangles, ΔABD and ΔCBD.
We will start with ΔABC.
∠B = 180 - (∠A+∠C) = 180 - (21+19) = 140
Now using sine law, we can find lengths a and b.
According to sine law,
b/sin21 = a/sin 19 = 600/sin 140
From this,
b/sin 21 = 600/sin 140
b/0.36 = 933.43
b = 336.03ft
Also,
a/sin 19 = 600/sin 140
a/0.33 = 933.43
a = 308.03ft
Now using ΔABD,
sin 21 =h/a
0.36 = h/308.03
h = 110.89 ft
Therefore after finding the sides of the triangle using sine law, we found that the height of the flagpole is found to be 110.89 ft.
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i need help guysss
schoology
Solving an equation we will see that the measure of angle a is 68°.
How to find the measure of the missing angle?We want to find the measure of angle a. On the image we can see that we have 3 angles, and the sum of these 3 angles should be equal to 180°, then we can write the equation:
28° + 90° + a = 180°
(the 90° angle is the one with the square).
Solving that equation for a, we will get:
a = 180° - 90° - 28°
a = 90° - 28°
a = 62°
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SOMEONE HELP URGENT PLS
20 POINTS AND BRAINLEST
A graph which represents the solution to this system of inequalities include the following: graph D.
How to graph the solution to this system of inequalities?In order to to graph the solution to the given system of inequalities on a coordinate plane, we would use an online graphing calculator to plot the given system of inequalities and then take note of the point of intersection;
y ≤ 3x - 4 .....equation 1.
4x + 2y < 6 .....equation 2.
Based on the graph (see attachment), we can logically deduce that the solution to the given system of inequalities is the shaded region below the solid and dashed line, and the point of intersection of the lines on the graph representing each, which is given by the ordered pair (1.4, 0.2).
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