Answer:
1 = 36
2. = 32
3 = 10
4.= 21
5. = 14
6 =7456200
Step-by-step explanation:
need help with problem 8
Hence, a 93% confidence range for the actual proportional difference between the two populations equation (represented by the two samples) is between -0.086 and 0.142.
What is the equation?A mathematical equation connects two statements with the equals sign (=), which stands for equivalence. The equivalence of two mathematical propositions is established by a mathematical assertion that is utilized in algebraic equations. For instance, the equal sign separates the numbers 3x + 5 and 14 in equation 3x + 5 = 14. Use a mathematical formula to understand the relationship between the two sentences written on opposite sides of a letter. Usually, the program's particular logo matches it. A good example is 2x - 4 = 2.
For the initial example:
Sample proportion: 0.649 (p1 = 24/37)
Standard deviation SE1 is equal to
[tex]\sqrt{(p^1*(1-p^1))} /n1=\sqrt{(0.649*(1-0.649))/37)0.087}[/tex]
Regarding the second example:
P2 = 54/87 0.621 is the sample proportion.
The standard deviation SE2 is equal to
[tex]\sqrt{(p^2*(1-p^2))} /n2=\sqrt{(0.621*(1-0.621))/87)0.72}[/tex]
The crucial value for a 93% confidence interval has to be calculated next. We may use the conventional normal distribution and large sample size to obtain the z-value that represents the center 93% of the distribution:
[tex]1.812z=invNorm(\frac{1+0.93}{2} )[/tex]
We can finally determine the confidence interval:
CI is equal to (p1-p2) z*sqrt(SE12 + SE22)
CI is calculated as (0.649 - 0.621) 1.812*sqrt(0.0872 + 0.0722)
CI = 0.028 ± 0.114
CI = (−0.086, 0.142)
The real proportional difference between the two populations (represented by the two samples) thus lies between -0.086 and 0.142, with a 93% confidence interval.
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what is 60 percent of 24
Answer:
14.4
Step-by-step explanation:
=24 * 60/100
=14.4
Answer:
14.4
Step-by-step explanation:
[tex]\frac{24}{10} = 10[/tex]% of 24
6[tex]\frac{24}{10} = 60[/tex]% of 24
PLEASE HELP ASAP NOWS YOU CHANCE FOR BRANLIST AND POINTS Polygon JKLM is drawn with vertices J(-4,-4), K(-4, -6), L(-1, -6), M (-1, -4). Determine the image coordinates of L' if the preimage is reflected across y =
-2. OPTIONS ARE BELOW
L'(-3, 6)
OL'(-1,6)
OL'(-1, 2)
OL(1, 2)
The correct answer is (C) OL'(-1, 2) - This point is on the reflected line y=-2, but its y-coordinate is not consistent with the reflection of L. The correct y-coordinate is -4.
What is line?
A one-dimensional geometric figure that consists of infinitely many points arranged in a straight path or direction.
In this case, we are reflecting across the line y = -2, which is two units below the x-axis. Therefore, the y-coordinate of each point in the preimage will be changed by 2 units after reflection.
The coordinates of L are (-1, -6), and after reflecting across y = -2, the y-coordinate will become
-6 + 2 = -4
Therefore, the image of L, L', will have coordinates (-1, -4).
Looking at the given options:
A. L'(-3, 6) - This point is not on the reflected line y=-2, so it cannot be the reflection of L.
B. OL'(-1,6) - This point is above the reflected line y=-2, so it cannot be the reflection of L.
C. OL'(-1, 2) - This point is on the reflected line y=-2, but its y-coordinate is not consistent with the reflection of L. The correct y-coordinate is -4.
D. OL(1, 2) - This point is not on the reflected line y=-2, so it cannot be the reflection of L.
Therefore, the correct answer is option C: L'(-1, -4).
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Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of function g if g(x) = f(x) − 11? A. It is the graph of f(x) where the slope is decreased by 11. B. It is the graph of f(x) translated 11 units down. C. It is the graph of f(x) translated 11 units up. D. It is the graph of f(x) where the slope is increased by 11.
The right response is B. It is the graph of f(x) scaled down by 11 units.
For any given value of x, the output of f(x) is subtracted by 11 to get the function g(x) = f(x) - 11.
The result is the same as the input for the function f(x) = x. Thus, if we take 11 out of the result, we get:
g(x) = f(x) - 11 = x - 11
In other words, the graph of g(x) is the graph of f(x), 11 units lower.
Thus, assertion B is the correct one. It is the graph of f(x) scaled down by 11 units.
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Please help on this fast
The table that shows a proportional relationship is Table A.
What is a proportional relationship ?A proportional relationship is a type of relationship between two variables in which the ratio of their values remains constant. In other words, as one variable increases or decreases, the other variable also increases or decreases in proportion to it.
In table A, we see that :
= 150 / 3
= 50
= 200 / 4
= 50
= 250 / 5
= 50
Every single value of y, gives the same value of x so this means that the table shows a proportional relationship.
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Ron is a huge golfer and he is interested in purchasing a new brand of golf balls that claim to extend his driving
range. Ron sets up an experiment where he will test these new golf balls against the current golf balls he uses to
see if his driving distance had increased. He will hit an SRS of 30 new golf balls and record the average range
and then will hit an SRS of 30 current golf balls and record the average range. He will then compare the
averages to see if there is a difference between the two true distances.
11) What type of study is being conducted by Ron and, of the following, which is the appropriate t-
interval for inference?
(A) A completely randomized design and a t-interval for a difference between means for independent samples
(B) A completely randomized design and a t-interval for a mean difference
(C) A matched-pairs design and a t-interval for a difference between means for independent samples
(D) A matched-pairs design and a t-interval for a mean difference
(E) An observational study and a t-interval for a difference between means for independent samples
12) The following is a table of his results.
New Golf Balls
Old Golf Balls
¿(yards)
203.5
197 4
S, (yards)
5.6
10.3
We set up our hypothesis to see if there is a significant difference in mean driving distance between the new
golf balls and the old golf balls. Based on our data, what is the appropriate t-statistic?
(A) 1.01
(B) 1.55
(C) 1.98
(D 2.85
(E) 3.33
13) Which of the following is a true statement about the study being conducted by Ron?
(A) Because this is an experiment, the random condition was violated due to no random assignment.
(B) Because this is an experiment, the fact that an SRS of balls was taken is insignificant.
(C) The central limit theorem tells us that the sampling distribution of driving distance for each of the individual
samples of balls will be approximately normal.
(D) The central limit theorem tells us that as long as our sample size is above 30, the population distribution
will be approximately normal.
(E) The results of this study will be meaningless because it was not double-blind
11) (A) a t-interval for a difference between means for independent samples.
12) the appropriate t-statistic is (C) 1.98.
13) option (c)
What is the central limit theorem?The central limit theorem is a principle in probability theory that states that the distribution of sample means will eventually approximate a normal distribution as the sample size becomes larger.
11) The type of study being conducted by Ron is a completely randomized design, where he randomly assigns the two types of golf balls (new and current) to two separate groups and then compares the mean driving distances between the two groups.
The appropriate t-interval for inference is (A) a t-interval for a difference between means for independent samples.
12) To test the hypothesis of whether there is a significant difference in mean driving distance between the new golf balls and the old golf balls, we need to calculate the appropriate t-statistic.
The formula for the t-statistic for a difference between means for independent samples is:
[tex]t = (x_1 - x_2) / [s1^2/n1 + s_2^2/n_2]^{0.5}[/tex]
where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes for the two groups.
Using the given data, we have:
x1 = 203.5 yards, x2 = 197.4 yards
s1 = 5.6 yards, s2 = 10.3 yards
n1 = n2 = 30
Substituting these values into the formula, we get:
[tex]t = (203.5 - 197.4) / [(5.6)^2/30 + 10.3^2/30]^{0.5} = 1.98[/tex]
Therefore, the appropriate t-statistic is (C) 1.98.
13) The correct statement about the study being conducted by Ron is (C) The central limit theorem tells us that the sampling distribution of driving distance for each of the individual samples of balls will be approximately normal.
Hence, The answers to the question:
11) (A) a t-interval for a difference between means for independent samples.
12) the appropriate t-statistic is (C) 1.98.
13) option (c)
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Answer: c
Step-by-step explanation:
A retailer buys merchandise from a supplier with an invoice amount of $12,400. The terms of the sale are 6/20, n/30. What is the net amount due (in $) on the order if the bill is paid by the 20th day?
If the retailer pays the invoice within 20 days and takes the discount, the net amount due is $11,656.
The sale's "6/20, n/30" clause allows the retailer to choose between paying the invoice in full within 30 days or taking advantage of a 6% discount if they do it within 20 days. If the bill is paid by the 20th day, we can determine the net amount owed as follows:
Then, we multiply the invoice amount by the discount rate to determine the amount of the discount:
Discount: $744 ($12.400 x 0.06)
The amount owed if the discount is taken is then determined by deducting the discount from the invoice amount:
Discounted amount due: $12,400 - $744 = $11,656
The net amount owed is therefore $11,656 assuming the store pays the invoice within 20 days and applies the reduction.
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Neo leaves home at 6:45 to drive to work. Neo drives a distance of 45 miles.Neo thinks he drives of an average speed of 30 miles per hour.
Neo is correct what time would he arrive at work ?
The time at which Neo reaches the work destination is A = 8 : 15 AM
What do you mean by an Equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.
It displays the similarity of the connections between the phrases on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.
Given data ,
Let the time at which Neo reaches the work destination be A
Now , the time at which Neo leaves home = 6 : 45 AM
And , the distance between Neo and work = 45 miles
where the speed of Neo is S = 30 miles per hour
So , the distance traveled by Neo in 1 hour = 30 miles
The distance traveled by Neo in 1.5 hours = 45 miles
Therefore , the time required by Neo to reach office is 1.5 hours
And , the time at which Neo reaches the work destination A = 6 : 45 AM + 1.5 hours
On simplifying the equation , we get
The time at which Neo reaches the work destination A = 8 : 15 AM
Hence , the equation is A = 8 : 15 AM
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Enola is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if she flips a coin and spins a spinner with 5 equal-sized sections labeled Monday, Tuesday, Wednesday, Thursday, Friday?
The number of possible outcomes is 10.
Finding the Number of outcomes:To find the number of possible outcomes find the number of outcomes when the coin is flipped and the number of outcomes when the spinner is spinning.
Multiply the number of outcomes from the coin by the number of outcomes from the spinner.
Here we have
Enola is designing a new board game,
She flips a coin and spins a spinner with 5 equal-sized sections labeled Monday, Tuesday, Wednesday, Thursday, Friday
No of possible outcomes when a coin is flipped = 2 [Head and Tail]
No of possible outcomes when she spins a spinner = 5
[ i.e Monday, Tuesday, Wednesday, Thursday, Friday ]
Hence, No of out comes = 2 × 5 = 10
Therefore,
The number of possible outcomes is 10.
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on an auto assembly line, every third car is green. Every fourth car is a convertible
Of the first 100 vehicles, there are nine convertible green cars.
Explain about the sequence of number?A succession or an ordered set of numbers regulated by a pattern or rule is referred to as a number sequence. Terms are a group of numbers in a sequence. A sequence with no end is referred to as a finite sequence, whereas an infinite sequence is one that never comes to a finish.The sequence of green cars:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99
The sequence of convertible cars:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100.
Convertible and Green cars (in the very first 100 cars):
12, 24, 36, 48, 60, 72, 84, and 96.
Thus, of the first 100 vehicles of auto assembly line, there are nine convertible green cars.
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The complete question is-
On an automobile assembly line, every third car is green. Every fourth car is a convertible. How many cars out of the first 100 will be green convertibles?
1) Write an algebraic expression, The quotient of g and 4 added to 15
2) Write an algebraic expression, 6 minus the difference of y and 3
3) Write an algebraic expression, the product of a number d and 8
The algebraic expressions for the given questions are found as:
1) g/4 + 15.
2) 6 - y + 3
3) d * 8
What are algebraic expressions?
A mathematical expression made up of variables, constant algebraic numbers, and algebraic operations are known as an algebraic expression. Everything with a variable value is anything whose value changes over time. Variables in expressions are often represented by letters of the alphabet. Finding the simplified term of the given expression is the goal of simplifying the algebraic expression. We must first understand how to join like terms, factor a number, and the order of operations before we can factorise or simplify the expression. When like terms are combined, the constant terms are divided for the purpose of simplicity and the variables with the same degree are grouped together.
1) The quotient of g and 4 is given by g/4.
Now, this is added to 15.
So the algebraic expression is g/4 + 15.
2) The difference between y and 3 is y - 3.
Now from 6, this difference is subtracted.
So the expression becomes,
6 - (y-3) = 6 - y + 3
3) The product of two numbers is found by multiplying the numbers.
So the expression is :
d * 8
Therefore the algebraic expressions for the given questions are found according to the given statements.
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Find the missing angle
Answer:
55
Step-by-step explanation:
The ? angle is 55 degrees since every triangle's angles add up to 180 degrees. We have 2 angles, one with 70 and another with 55, so we add them to get 125. Then we subtract 125 from the total angle of a triangle, 180-125, to get 55.
the answer is 55
they have the same degrees hope this helps
the width of a rectangle is 2 units less than the length. The area of the rectangle is 15 square units. What is the length of the rectangle
Answer: 5
Step-by-step explanation:
area = width x length
15 = w x w-2
15 = 5 x 3
3 is 2 less than 5, and if you multiply them together, you get the area, 15
Please help with this thank you
The equation of the line crossing (3, 1 / 2)(5, 5) is y = 9 / 4 x - 25 / 4.
How to find equation of a line?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slope of the lineb = y-interceptHence, let's find the equation of the line crossing (3, 1 / 2)(5, 5).
m = 5 - 1 / 2 / 5 - 3
m = 9 / 2 × 1 / 2
m = 9 / 4
Hence, let's find the y-intercept using (5, 5)
y = 9 / 4 x + b
5 = 9 / 4(5) + b
5 - 45 / 4 = b
b = 20 - 45/ 4
b = - 25 / 4
Therefore, the equation of the line is y = 9 / 4 x - 25 / 4.
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solve for x. 4(x+56.5)=30x-112
Answer:
x = 13
Step-by-step explanation:
Let's simplify and solve for x:
4(x+56.5) = 30x - 112
First, we distribute the 4:
4x + 4(56.5) = 30x - 112
Simplifying the expression:
4x + 226 = 30x - 112
Now we move all the x terms to one side and all the constants to the other:
226 + 112 = 30x - 4x
338 = 26x
Finally, we solve for x by dividing both sides by 26:
x = 13
Therefore, the solution to the equation 4(x+56.5)=30x-112 is x = 13.
Answer:
x=9.94
Step-by-step explanation:
4x + 226 = 30x - 112
226+112 = 34x
338 = 34x
338/34=x
9.94=x
pls help i will give 10 points to the first person to answer this question
The coordinates of the points on the number line are given as follows:
A = -2/3.B = -1/6.C = 1/2.D = 4/3.How to obtain the coordinates on the number line?Point C is exactly halfway between 0 and 1, hence it's coordinate is given as follows:
C = 0.5.
C is also the third dot between 0 and 0.5, hence the amount represented by each space is given as follows:
0.5/3 = 1/6.
Point B is one space to the left of 0, hence it's coordinate is given as follows:
B = -1/6.
Point A is three spaces to the left of point B, hence it's coordinate is given as follows:
A = -1/6 - 3 x 1/6 = -4/6 = -2/3.
Point D is two spaces to the right of 1, hence:
D = 1 + 2x 1/6 = 1 + 1/3 = 4/3.
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Three people spend money on a vacation. The expression −1,0263 represents the amount of money each person spends on the vacation. Which expression is equivalent to −1,0263 ?
Answer:-(-1,026/3
Step-by-step explanation:
What is the combined weight of all the loaves of bread? Show your work.
The mass of each bun is 50g.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that the total mass of 2 loaves of bread and 5 buns is 650g.
The 2 loaves of bread weigh 400 g.
We need to find the mass of each bun.
2 loaves of bread + 5 buns = 650g
2 loaves of bread = 400g
5 buns = 650g - 400g
=250g
1 bun = 250/ 5
= 50g
The mass of each bun is 50g.
Hence, the mass of each bun is 50g.
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Complete question
The total mass of 2 loaves of bread and 5 buns is 650 g. The 2 loaves of bread weigh 400 g. What is the mass of each bun?
Maria and Connor are doing yard work for a neighbor. They make a total of $595.54. Since Connor works more hours than Maria, Connor gets 69% of the money. About how much (in whole
dollars) does Connor make?
Connor makes about
Answer: Since Connor gets 69% of the money, Maria gets the remaining 31%:
100% - 69% = 31%
Let's first find out how much money Maria makes:
Maria's share = 31% of $595.54
Maria's share = 0.31 x $595.54
Maria's share = $184.61
Now, to find out how much Connor makes, we can subtract Maria's share from the total:
Connor's share = Total - Maria's share
Connor's share = $595.54 - $184.61
Connor's share = $410.93
Therefore, Connor makes about $410.93 (rounded to the nearest dollar).
Step-by-step explanation:
Sandra read 200 pages over x days. How would you show how many
pages she read each day?
Solve ASAP
Answer:
200 x 7 = 1,400 x = 7 because there are 7 days in a week
Step-by-step explanation:
Which of the lines or segments below is secant to circle
The lines or segments which are secant to a circle are:
AK, TW, RN & UN
What is secant of the circle?A line that crosses a circle at two different locations is referred to as a "secant of a circle" in geometry. The Latin verb "secare," which meaning "to cut," is where the English term "secant" originates.
More technically, a secant of a circle is a line that crosses it twice, whereas a tangent of a circle is a line that crosses it only once. A circle's diameter is a chord that runs through its center, whereas a chord of a circle is a line segment connecting two locations on the circle.
Given that,
Two circle which contains various tangents, normal & secants
As we know from the definition of secant it intersect the circle at two points,
Line segments AK, TW, RN & UN are intersecting the circle at two points,
so all this segments are secant of the circle.
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Which first step could you take to solve this system using elimination?
Equation #1: 2x + 18y = -9
Equation #2: 4x + 18y = -27
(Choose all correct answers)
Multiply equation #1 by 2
Multiply either equation by -1
Multiply equation #1 by -2
Multiply equation #1 by -3
Answer:
Step-by-step explanation:
To use elimination method, we need to eliminate one of the variables (x or y) by adding or subtracting the two equations. To do this, the coefficients of one of the variables in the two equations should be the same or opposite.
Looking at the two equations:
Equation #1: 2x + 18y = -9
Equation #2: 4x + 18y = -27
We can see that the coefficients of y are already the same in both equations. So, we can eliminate y by subtracting Equation #1 from Equation #2.
However, to do this we need to make sure that the coefficients of x in the two equations are opposites, i.e., one is positive and one is negative.
Therefore, the first step we could take to solve this system using elimination is to multiply Equation #1 by -2 to get:
-4x - 36y = 18
Now the coefficients of x in the two equations are opposites, so we can subtract Equation #1 from Equation #2 to eliminate y and solve for x.
So, the correct answer is:
Multiply equation #1 by -2.
A herd of elk is released onto state game lands. The expected population P of the herd can be modeled by the equation below where t is the time in years since the initial number of elk were released. P = (10 + 3.3t)/(1 + 0.1t)
(a) State the domain of the model.
t ≥ 0
t ≠ 10
t < 0
t > 0
t ≤ 0
all real numbers
t ≠ -10
(b) Find the initial number of elk in the herd. ________
(c) Find the populations of elk after 25, 59, and 113 years. (Round your answers to the nearest integer.) _____________
(d) Is there a limit to the size of the herd? If so, what is the expected population? (Round your answer to the nearest integer. If there is no limit, enter NONE.) ____________
Since the denominator of the expression (1 + 0.1t) cannot be zero, the domain of the model is between t = 0 and t = -10.
How Can I Determine an Equation's Domain and Range?In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range after we identify g's domain (y).
(b) We must assess the model at t = 0 in order to determine the starting number of elk in the herd:
P = (10 + 3.3t)/(1 + 0.1t)
P = (10 + 3.3(0))/(1 + 0.1(0))
P = 10/1
P = 10
(c) We can easily enter the relevant values of t into the model to determine the populations of elk after 25, 59, and 113 years, then round the results to the nearest integer.
When t = 25:
P = (10 + 3.3t)/(1 + 0.1t)
P = (10 + 3.3(25))/(1 + 0.1(25))
P ≈ 47
When t = 59:
P = (10 + 3.3t)/(1 + 0.1t)
P = (10 + 3.3(59))/(1 + 0.1(59))
P ≈ 189
When t = 113:
P = (10 + 3.3t)/(1 + 0.1t)
P = (10 + 3.3(113))/(1 + 0.1(113))
P ≈ 458
(d) We can use the expression's limit as t approaches infinity to determine the expected population limit:
lim P as t → ∞ = lim (10 + 3.3t)/(1 + 0.1t) as t → ∞
Using L'Hopital's rule, we can find that the limit is equal to:
lim P as t → ∞ = lim 3.3/0.1 as t → ∞
lim P as t → ∞ = 33
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Your friend buys 1 8/10 tenths of a pound of bananas. If each pound cost $4.10, how much do they pay for her bananas?
Answer:
Below
Step-by-step explanation:
1 8/10 = 18/10
18 / 10 pound * $ 4.10 / pound = (18 * 4.1) / 10 = 73.8 /10 = $ 7.38
( see how the unit 'pound' cancels out and you are left with $ ???)
PART 2: TABLE 1: Mr. Flynn found that his car can drive 12,5km for every litre of petrol it consumes. This helps him to be sure that he has enough petrol when driving certain distances - due to the nature of his work. The table below represents the car's petrol consumption. The extreme petrol price per litre of R22,50 also impacts Mr. Flynn's travelling. Study the table and answer the questions that follow. 2.1 2.2 2.3 4 2.4 PETROL CONSUMPTION VERSUS TRAVEL DISTANCE (OBSERVABLE PATTERN) DISTANCE TRAVELLED PER LITRE PETROL CONSUMED Litres of Petrol 0 1 2 3 B 5 6 7 8 Distance to Travel (km) A 12,5 25,0 37,5 50,0 62,5 C 87,5 100 Describe the general relationship between distance travelled and litres
The proportional relationship between distance traveled and liters spent is given as follows:
y = 0.08x.
What is a proportional relationship?A proportional relationship is defined by a linear model with intercept of zero as follows:
y = kx.
In which k is the constant of proportionality.
Mr. Flynn found that his car can drive 12,5km for every litre of petrol it consumes, hence the constant is given as follows:
k = 1/12.5
k = 0.08.
Then the equation is given as follows:
y = 0.08x.
In which:
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if you don't know this circumference but you do know that 75% of the circumference is 6 in what would circumference be
Answer:
circumference = 8 inches
Step-by-step explanation:
75% = 75/100 = 3/4
Let C be the circumference
3/4 C = 6
Multiply both sides by 4/3
C =
PRYZ is a square. If RK = 5, RY=5, find each measure. KZ= ? YP = ? m<PRZ =? m<ZYKZ=?
The solution is, in PRYZ square, the value of m∠YKZ = 90.
What is a square?A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.
here, we have,
Remember that
In a Square
All sides are equal
Diagonals bisect each other perpendicularly
so
Find out KY
In the right triangle RYK
Applying the Pythagorean Theorem
RY^2=RK^2+KY^2
substitute given values
13^2=5^2+KY^2
KY^2=13^2-5^2
KY^2=144
KY=12
Find out PK
Remember that
Diagonals bisect each other perpendicularly
that means
PK=KY=12
Remember that
Diagonals bisect each other perpendicularly
so, that means
m∠YKZ = 90
Hence, The solution is, in PRYZ square, the value of m∠YKZ = 90.
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The family likes peaches and other fruits. The local farmer’s market is selling fresh peaches at a discounted price. If the farmer’s market sold 35% of its produce and has 260 peaches remaining, how many peaches did it originally have on hand? Show all your work and explain how you used equivalent ratios to solve the problem.
The farmer's market originally had 400 peaches on hand.
What is an equation?
An equation is a mathematical statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and radicals.
Let's use x to represent the original number of peaches the farmer's market had on hand.
We know that the farmer's market sold 35% of its produce, which means it sold 0.35x peaches. The remaining number of peaches can be calculated by subtracting the number of peaches sold from the original number of peaches:
remaining peaches = x - 0.35x
We also know that there are 260 peaches remaining, so we can set up an equation:
260 = x - 0.35x
Simplifying this equation, we can combine like terms:
260 = 0.65x
To solve for x, we need to isolate the variable by dividing both sides by 0.65:
x = 260 / 0.65
x = 400
Therefore, the farmer's market originally had 400 peaches on hand.
To explain how we used equivalent ratios, we used the fact that the farmer's market sold 35% of its produce. This can be represented as a ratio of 35/100 or 0.35. We then used this ratio to find the number of peaches sold, which is 0.35x. We also used the fact that the remaining peaches are the original peaches minus the peaches sold, or x - 0.35x. Finally, we set up an equation using the remaining peaches and solved for x to find the original number of peaches.
Hence, the farmer's market originally had 400 peaches on hand.
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Nelda needs to wrap a holiday gift box. The box is in the shape of a rectangular prism with the dimensions shown.
What is the total surface area of the gift box?
Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.
Answer:
[tex]416 \;in^2[/tex]
Step-by-step explanation:
The surface area of the rectangular prism
[tex]S = 2(lw + lh + wh)[/tex]
where
l = length = 12 in
w = width = 10 in
h = height = 4 in
Therefore
[tex]S = 2(12\cdot 10 \;+ \; 12\cdot 4 \;+\;10 \cdot 4)\\\\= 2(120 + 48 + 40)\\\\= 2 (208)\\\\= 416 \: in^2[/tex]
Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options.
18 x minus 15 = 72
50 x minus 25 = 72
18 x minus 9 = 72
3 (6 x minus 3) = 72
x = 4.5
The equations that have the same value of x as the given equation are:
18x - 9 = 72
3(6x - 3) = 72
x = 4.5
The correct options are the third, fourth, and fifth options
Determining the equations that have the same value of xFrom the question, we are to determine the equations that have the same value of x as the given equation
To solve the given equation, we can begin by simplifying it:
3/5 (30 x - 15) = 72
Multiplying both sides by 5/3, we get:
30 x - 15 = 120
Adding 15 to both sides, we get:
30 x = 135
Dividing both sides by 30, we get:
x = 4.5
Now, to check which equations have the same value of x as the above result, we can substitute x = 4.5 in each option and see which ones result in a true statement.
18 x - 15 = 72Substituting x = 4.5, we get:
18(4.5) - 15 = 72
81 - 15 = 72
This is not a true statement, so this option is not correct.
50 x - 25 = 72Substituting x = 4.5, we get:
50(4.5) - 25 = 72
225 - 25 = 72
This is not a true statement, so this option is not correct.
18x - 9 = 72Substituting x = 4.5, we get:
18(4.5) - 9 = 72
81 - 9 = 72
This is a true statement, so this option is correct.
3(6x - 3) = 72Substituting x = 4.5, we get:
3(6(4.5) - 3) = 72
3(24) = 72
This is a true statement, so this option is correct.
x = 4.54.5 = 4.5
This is a true statement, so this option is correct.
Hence, the equations are:
18x - 9 = 72
3(6x - 3) = 72
x = 4.5
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