18 points in 15 hour is greater than 45 points in 36 hours.
What is unit rate?The unit rate compares a certain number of units of one quantity to units of another quantity. In other words, the second quantity in the comparison is always 1.
45 points in 36 hours and 18 points in 15 hours.
Points per hour
45 points in 36 hours is given by,
[tex]\frac{45}{60} =1.25[/tex] points.
18 points in 15 hours is given by,
[tex]\frac{18}{15}[/tex] = 1.2 points.
On comparing these points 1.2 > 1.25.
Hence, 18 points in 15 hour is greater than 45 points in 36 hours.
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Which two sets of values make the inequality 3(n – 2) ≤ 2n – 3 true?
A. {−2, −1, 3}
B. {−2, −1, 4}
C. {−1, 0, 3}
D. {−1, 1, 4}
E. {1, 0, 5}
The vet says that raise puppy will grow to be at most 28 inches tall raise. Puppy is currently 1 foot tall how much more will the puppy grow?
Write an inequality to solve the problem
Answer:
16 inches
Step-by-step explanation:
28 - 12 = 16 inches
1 foot = 12 inches
Find the sample variance and standard deviation.
23, 16, 5, 7, 11 q
OA. s² =
2
S
OB. 0²=
The sample variance and the standard deviation are 52.8 and 7.26
How to determine the sample variance and standard deviationFrom the question, we have the following parameters that can be used in our computation:
23, 16, 5, 7, 11
Calculate the mean
Mean = (23 + 16 + 5 + 7 + 11)/5
Mean = 12.4
The standard deviation is
SD = √[Sum of (1 - Mean)²]/[N - 1]
So, we have
SD = √[(23 - 12.4)² + (16 - 12.4)² + (5 - 12.4)² + (7 - 12.4)² + (11 - 12.4)²]/[5 - 1]
This gives
SD = √211.2/4
So, we have
SD = √52.8
SD = 7.26
Hence, the standard deviation is 7.26
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A sign in the shape of a circle has a radius of 15 cm. What is the area of the sign? Use 3.14 for pi.
Answer:
The area of the sign is 706.5 cm^2.
Step-by-step explanation:
We know,
The formula of area of a circle,
A = πr^26
Here A is area and r is radius.
Here we have radius is 15 cm, so we can put the values in the above equation and find the area,
A = π * 15^2
A = 3.14 * 225
A = 706.5
The area of the sign is 706.5 cm^2.
decimal of 3\4 and percent
Equivalence means to be same, whether it be value, temperature, size, etc.
First, let's convert [tex]\frac{3}{4}[/tex] into a different fraction.
[tex]\frac{3}{4}[/tex] = [tex]\frac{75}{100}[/tex]We know this because each side of the fraction [tex]\frac{3}{4}[/tex] can be multiplied by 25 to get [tex]\frac{75}{100}[/tex].
3 × 25 = 754 × 25 = 100Now that we know this, we can convert the fraction [tex]\frac{75}{100}[/tex] into a percentage.
What is a percentage?A percentage is a ratio, or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.
if we know that percentages are expressed as a fraction of 100, we know that [tex]\frac{75}{100}[/tex] is equal to %75.
To convert percentages into decimals, we can just take the percentage (%75) and fit it into 0.00, making it 0.75.
Therefore, the fraction [tex]\frac{3}{4}[/tex] as a percentage is %75, and as a decimal it is 0.75.
Miguel was selling apples, plums, and peaches at the local farmer’s marker. He sold 18 more
pounds of apples than pounds of plums. He sold 9 pounds less of peaches than pounds of
plums. He sold a total of 69 pounds of fruit. How many pounds of each fruit did he sell?
Answer:
He sold 32 pounds of apples, 14 pounds of plums and 23 pounds of peaches.
Step-by-step explanation:
Let:
x = Mass of Apples (pounds)
y = Mass of plums (pounds)
z = Mass of peaches (pounds)
He sold 18 more pounds of apple than pounds of plums: [tex]x = 18 + y[/tex]
He sold 9 less pounds of peaches than pounds of plums: [tex]z - 9 = y[/tex]
He sold a total of 69 pounds of fruit: [tex]x + y + z = 69[/tex]
We have 3 unknown variables, therefore a system of 3 linear simultaneous equations:
[tex]x = 18 + y[/tex] ——- (equation i)
[tex]z - 9 = y[/tex]
∴ [tex]z = 9 + y[/tex] ——— (equation ii)
[tex]x + y + z = 69[/tex] ——- (equation iii)
The above linear simultaneous equations can be solved by Substitution Method:
Substitute (equation i) and (equation ii) into (equation iii) to solve for y. Expand the parenthesis and bring all the like terms together. y has to be made the subject of the equation:
[tex](18 + y) + y + (y + 9) = 69[/tex]
= [tex]18 + y + y + y + 9 = 69[/tex]
= [tex]y + y + y = 69 - 18 - 9[/tex]
= [tex]3y = 42[/tex]
= [tex]y = \frac{42}{3}[/tex]
∴ y = Mass of plums = 14 pounds
Substitute the calculated value of y into the other two equations to solve for x and for z:
[tex]x = 18 + (14)[/tex]
∴ x = Mass of apples = 32 pounds
[tex]z = 9 + (14)[/tex]
∴z = Mass of peaches = 23 pounds
emma has 0.5 lb of sugar. How much water would she add to make the following concenstractions? Tell Emma how much syrup she would have each case. 50% syrup
To make the concentration of 50% syrup,
she needs to add 0.5 lb of sugar.
What is a percentage?A percentage is a ratio or number that may be expressed as a fraction of 100. Moreover, it is denoted by the sign "%."
Given:
Emma has half a pound of sugar.
To make the concentration of 50% syrup:
Let n be the required amount.
In decimals, 50% is 0.5.
Applying the percentage formula;
we get,
[tex]\frac{0.5}{n + 0.5} \cdot 100 = 50[/tex]
Applying cross multiplication,
we get,
[tex]\frac{0.5}{n + 0.5} = 0.5[/tex]
0.5 = 0.5(n + 0.5)
1 = n + 0.5
n = 1 - 0.5
n = 0.5 lb.
Therefore, she would have 0.5 + 0.5 = 1 pound of sugar.
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is 5.2481 a ratinal number
Answer:
Step-by-step explanation:
Rational numbers are numbers that can be written in the form pq, where p and q are integers and q≠0. The difference between rational numbers and fractions lies in the fact that fractions cannot have negative numerator or denominator.
so, yes.
Find the slope of a line parallel to 25x-5y=-10
.
The slope of a line parallel to another line will have the same slope as the original line. To find the slope of the line 25x - 5y = -10, we need to rearrange the equation into the slope-intercept form y = mx + b, where m is the slope.
First, we'll isolate y:
25x - 5y = -10
5y = 25x + 10
y = (25/5)x + 2
So the slope of the line 25x - 5y = -10 is m = 25/5 = 5.
Therefore, a line parallel to 25x - 5y = -10 will have a slope of m = 5.
Tarzan loaded 14 trucks every 35 minutes. At that rate how long in minutes will it take to load 8 trucks
someone help me please
Step-by-step explanation:
This symbol is signma, which is the sub of all the X's after plugging them into the equation.
Just to show the pattern, the first 3 numbers on your table are 15, 13, and 13... doing those 3 with Sigma, and simplifying
[tex]( {1 5 - 2)}^{2} + ({13 - 2)}^{2} + {(13 - 2)}^{2} [/tex]
[tex]169 + 121 + 121[/tex]
You would pretty much do that all the way down the list.
After doing so, we wind up with
15, 13, 13, 4, 19, 12, 6, 5, 14
[tex]169 + 121 + 121 + 4 + 289 + 100 + 16 + 9 + 144[/tex]
Adding these together gets your answer of:
[tex]973[/tex]
[tex]\frac{x+8}{3} =7\\[/tex]
Answer:
The solution is 13
Step-by-step explanation:
x+8/3 = 7
x+8 = 7×3
x+8 = 21
x = 21-8
x = 13
What is the y-intercept of the line perpendicular to the line y = 3/4x + 3 that includes the point (3, 1)?
Answer:
Step-by-step explanation:
perp.: -4/3
y - 1 = -4/3(x - 3)
y - 1 = -4/3x + 4
y = -4/3x + 5
y-int: (0, 5)
Patrick and Brooklyn are making decisions about their bank accounts. Patrick wants to deposit $300 as a principal amount with an interest of 3% compounded quarterly Brooklyn
wants to deposit $300 as the principal amount, with an interest of 5% compounded monthly Explain which method results in more money after 2 years Show all work
Answer:
To compare the amount of money that Patrick and Brooklyn would have after 2 years, we need to calculate the interest earned using each of their methods.
For Patrick, who deposited $300 with an interest rate of 3% compounded quarterly, the formula to calculate the amount after 2 years (8 quarters) is:
A = P(1 + r/n)^(nt)
Where:
P = principal amount ($300)
r = interest rate (3%)
n = number of times compounded per year (4)
t = time in years (2)
Substituting the values into the formula:
A = $300(1 + 0.03/4)^(4 * 2)
A = $300(1.0075)^8
A = $300 * 1.06173
A = $318.52
For Brooklyn, who deposited $300 with an interest rate of 5% compounded monthly, the formula to calculate the amount after 2 years (24 months) is:
A = P(1 + r/n)^(nt)
Where:
P = principal amount ($300)
r = interest rate (5%)
n = number of times compounded per year (12)
t = time in years (2)
Substituting the values into the formula:
A = $300(1 + 0.05/12)^(12 * 2)
A = $300(1.00417)^24
A = $300 * 1.09722
A = $328.17
Therefore, after 2 years, Brooklyn would have $328.17, which is more money than Patrick's $318.52.
The number of milligrams of Vitamin C from 100 different gummy vitamins sold in the world was collected.
Which graphical representation would be most appropriate for the data, and why?
Box plot, because the median can easily be determined from the large set of data
Stem-and-leaf plot, because you can see the shape of the data
Histogram, because it shows each individual data point
Bar chart, because the data is categorical
Box plot, because the median can easily be determined from the large set of data.
What exactly is a median?
The median is defined as the value in the centre of a given set of numbers or statistics. There are three main measures in mathematics that are used to calculate the average value for a given group of integers. They are the mean, the median, and the mode. These three indicators are known as central tendency measures. Mean computes the average value of the provided data. A median defines the midway value of the provided data. Mode defines the repeating value of the input data.
Now,
As, A box plot is a very visual means of displaying a concise overview of one or more sets of data. It is especially handy for quickly summarising and comparing several sets of findings from various trials. A box plot, at a glance, gives a graphical representation of the distribution of findings as well as indicators of symmetry within the data.
and it can handle a large set of data.
Hence,
Box plot, because the median can easily be determined from the large set of data.
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Answer:box plots
Step-by-step explanation:
i did it
Find the number of solutions for the given equation for 0° ≤ θ ≤ 360°.
sin2x - 2sinx - 3 = 0
1
2
3
4
0
The number of solutions to the trigonometric equation is; 1 solution which is x = 270°
How to find the trigonometric solution?The trigonometric equation is given as;
sin²x - 2sin x - 3 = 0
Now, factorizing this gives us;
(sin x - 3)(sin x + 1) = 0
Thus, we now have;
sin x - 3 = 0
sin x = 3
At this point, x has no real solution
For the second factor, we have;
sin x + 1 = 0
sin x = -1
x = sin⁻¹ -1
x = 270°
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A school is having a movie day. They are selling popcorn at the school for $0.50 per bag. If a student purchases popcorn with $5, how much popcorn would the student receive?
This student would receive 10 bag of popcorns.
How to determine the quantity of popcorn?Generally speaking, a unit price can be defined as the price that is being charged by a seller for the sale of a single unit of product.
In order to determine the quantity of popcorn, we would make use of the information provided about the unit price for one bag of popcorn by using the following mathematical expression;
Number of bag of popcorns = Cost of one bag of popcorn/Unit price
Substituting the given parameters into the mathematical expression above, we have the following;
Number of bag of popcorns = 5/0.50
Number of bag of popcorns = 10 bag of popcorns.
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How many cups will you get if you mix 2 gallons, 4 quarts, and 1 pint?
You will get
cups.
Answer: 50 Cups
Step-by-step explanation:
16 cups in a gallon. so times that by 2, which equals 32. There are four cups in one quart so times 4 by 4 which is 16 and add to 32. 16 + 32 = 48
Two cups in a pint so add 2 to 48 which is 50
Answer:
You will get 25 cups if you mix 2 gallons, 4 quarts, and 1 pint.
Step-by-step explanation:
To convert between gallons, quarts, and pints, we need to use the following conversions:
1 gallon = 4 quarts
1 quart = 2 pints
Here's the step-by-step process to convert the given volume to cups:
Convert gallons to quarts: 2 gallons * 4 quarts/gallon = 8 quarts
Add the number of quarts from step 1 to the number of quarts given: 8 quarts + 4 quarts = 12 quarts
Convert pints to quarts: 1 pint * 1 quart/2 pints = 0.5 quarts
Add the number of quarts from step 3 to the number of quarts from step 2: 12 quarts + 0.5 quarts = 12.5 quarts
Convert quarts to cups: 12.5 quarts * 2 cups/quart = 25 cups
Therefore, you will get 25 cups if you mix 2 gallons, 4 quarts, and 1 pint.
what decimal is equivalent to 29 11
Answer:
2.64
Step-by-step explanation:
3. Find the volume of a cone with radius 6 m and height 20 m
Answer: 753.98m³
Formula:V=πr2h3=π·62·203≈753.98224m³
A school newspaper reporter decides to randomly survey 13 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 23% of students attend Tet festivities. We are interested in the number of students who will attend the festivities. Part (a) Part (b) List the values that X may take on. O X =0, 1, 2..... 23 x = 1, 2, 3....23 x = 1, 2, 3....13 OX0.1.2..... 13 OO Part (c) Give the distribution of X. X-OX (0:0) Part (d) How many of the 13 students do we expect to attend the festivities? (Round your answer to the nearest whole number.) student(s) O Part (e) Find the probability that at most 3 students will attend. (Round your answer to four decimal places.) Part (0) Find the probability that more than 2 students will attend. (Round your answer to four decimal places.)
The probability that more than 2 students will attend is 0.9179.
Part (a) List the values that X may take on.
X may take on the values 0, 1, 2, 3, ..., 13.
Part (b) Give the distribution of X.
The distribution of X can be represented as follows: X-0:0, 1:0.23, 2:0.23, 3:0.23, 4:0.23, 5:0.23, 6:0.23, 7:0.23, 8:0.23, 9:0.23, 10:0.23, 11:0.23, 12:0.23, 13:0.23
Part (c) How many of the 13 students do we expect to attend the festivities? (Round your answer to the nearest whole number.)
We can expect 3 students to attend the festivities.
Part (d) Find the probability that at most 3 students will attend. (Round your answer to four decimal places.)
The probability that at most 3 students will attend is 0.6923.
Part (e) Find the probability that more than 2 students will attend. (Round your answer to four decimal places.)
The probability that more than 2 students will attend is 0.9179.
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Find side RT
10 m
13m
14 m
16 m
The side RT of the triangle is 13 m.
How to find the side RT of the triangle?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
The sine law is a mathematical formula used in trigonometry to relate the sides and angles of a triangle. The sine law states that:
a/sin(A) = b/sin(B) = c/sin(C)
where:
a, b, and c are the lengths of the sides of the triangle
A, B, and C are the angles opposite those sides
Using sine law:
RT/sin 34° = ST/sin 109°
RT/sin 34° = 22/sin 109°
RT = (22 * sin 34°)/(sin 109°)
RT = 13 m
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The entry ticket to a local museum costs $12 for an adult and $8 for a child. A group of 100 people paid an entry fee of $1,056. How many adults and how many children were there in this group?.
The number of adults and children in the group were 64 and 36 respectively by using an algebraic equation.
It is given that the entry ticket to a local museum costs $12 for an adult and $8 for a child. A group of 100 people paid an entry fee of $1,056.
Let the number of adults in the group = x
number of adults in the group = y
Total number of people paid an entry fee = 100
So the equation becomes : x + y = 100
or x = 100 - y
Cost for adult ticket = $12
Cost for child ticket = $8
Total entry fee paid = $1,056
Second equation = 12x + 8y = 1056
putting value of x from equation 1
12(100 - y) + 8y = 1056
1200 - 12y + 8y = 1056
4y = 144
y = 36
x = 100 - 36 = 64
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which answer is the right choice
7200+80x = 3200+120x
Reason:
Canton starts off with 7200 people. Add on 80x to represent the fact the town grows 80 people per year. That's how we end up with the expression of 7200+80x
Similarly, the expression 3200+120x represents the idea Holly Springs started off with 3200 people and grows at 120 people per year.
< Question 4, 1.2.23 >
points
O Points: 0 of 1
Use the method of successive differences to determine the next number in the given sequence.
7; 35; 173; 771; 2529; 6667; 15,095
Assuming that the pattern continues, the eighth term would be
The pattern does not have a consistency to get the differences
How to find the patternThe method of successive differences involves finding the difference between each consecutive term in a sequence, and then using those differences to find the next term.
Here's how the method would work for the sequence given:
7; 35; 173; 771; 2529; 6667; 15,095
Difference between terms:
28; 138; 598; 1758; 4138; 8428
Second difference between terms:
110; 460; 1160; 2380; 4290
Third difference between terms:
350; 700; 1220; 1910
Fourth difference between terms:
350; 520; 690
There is no consistency between the patterns.
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I need help solving part b)
The answers to the questions are:
a) P(A|B) = 1/3
b) P(B|A) = 1.15
c) A. A student given a $1 bill is more likely to have kept the money.
What is the probability?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
Because the probability of 0.659 is almost two times greater than 0.341
Assuming the following table:
Purchased Gum Kept the Money Total
Students Given 4 Quarters 25 19 44
Students Given $1 Bill 13 26 39
Total 38 45 83
a. find the probability of randomly selecting a student who spent the money, given that the student was given a $1 bill.
For this case let's define the following events
B= "student was given $1 Bill"
A="The student spent the money"
For this case we want this conditional probability:
P(A|B) = P(A And B) / P(B)
We have that
P(A) = 38/83, P(B) = 39/83
P(A And B) = 13/83
And if we replace we got:
P(A|B) = (13/83)/(45/83) = 13/39 = 1/3
b. find the probability of randomly selecting a student who kept the money, given that the student was given a $1 bill.
For this case let's define the following events
B= "student was given a $1 Bill"
A="The student kept the money"
P(A|B) = P(A And B) / P(B)
We have that
P(A) = 45/83, P(B) = 39/83
P(A And B) = 26/83
And if we replace we got:
P(B|A) = (45/83)/(39/83) = 45/39 = 1.15
c. what do the preceding results suggest?
For this case the best solution is:
A. A student given a $1 bill is more likely to have kept the money.
Because the probability of 0.659 is almost two times greater than 0.341
Hence, The answers to the questions are:
a) P(A|B) = 1/3
b) P(B|A) = 1.15
c) A. A student given a $1 bill is more likely to have kept the money.
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What might the composer do to write a piece with a carefree and ecstatic mood?
A. A lively accompaniment
B. Dissonant chords
C. A slow tempo
D. A minor key
Answer:
A. A lively accompaniment
Step-by-step explanation:
B. Dissonant - would most likely result in a eerie mood
C. A slow tempo - could result in melancholy or calm emotions
D. A minor key - could also result in melancholy emotions
Convert the complex number 2√2(cos 135° + i sin 135°) into rectangular
(standard) form. Express your answer in simplest radical form.
The solution to the complex number in rectangular form is; -2 + 2i
How to express complex number in rectangular form?The complex number is given as;
2√2(cos 135° + i sin 135°)
The standard form is a + bi.
The value of cos 135° is; -(√2)/2
The value of sin 135° is; (√2)/2
Plugging these values into the given equation is;
2√2(-(√2)/2 + ((√2)/2)i)
Expanding the bracket gives;
-2 + 2i
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Figure ABCD is a kite.
Find the value of x.
A
X =
= [?]
14x - 22
H
B
C
The value of x is equal to 8, in the equation 14x -22.
What is equation?An equation is a mathematical statement consisting of two expressions joined by an equal sign.
Solution:
The diagonals of the dragon intersect at right angles. This gives a solvable relationship for x.
setting the displayed dimensions correspond to 90° angular dimensions.
14x -22 = 90
You can solve this two-level linear equation in the usual way.
14x = 112. . . . . . Step 1, add the reciprocal of the constant to get just x
x = 112/14 = 8 . . . Step 2, divide by the factor of x
Hence, the value of x is 8.
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PLEASE I NEED HELP ASAP
A circle has a circumference of 21.98 inches. What is the diameter of the circle? (Use
3.14 for )
Answer:
Step-by-step explanation:
The formula for the circumference of a circle is C = 2 * π * r, where r is the radius of the circle. We can find the radius of the circle by rearranging the formula to r = C / (2 * π).
Substituting the given values into the formula, we get:
r = 21.98 inches / (2 * 3.14) = 21.98 inches / 6.28 = 3.50 inches
The diameter of the circle is equal to twice the radius, so we can find the diameter by multiplying the radius by 2:
d = 2 * r = 2 * 3.50 inches = 7.00 inches.
To find the diameter of a circle with a given circumference, you can use the following steps:
Define the formula for the circumference of a circle: The circumference of a circle is given by the formula C = 2πr, where π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.
Substitute the given circumference into the formula: If the circumference of the circle is 21.98 inches, we can substitute that into the formula to get 21.98 = 2πr.
Solve for the radius: To solve for the radius, we can divide both sides of the equation by 2π: 21.98 / 2π = r. Using 3.14 for π, this gives us 21.98 / (2 * 3.14) = r, which can be simplified to r = 2.01 inches.
Calculate the diameter: The diameter of a circle is twice the radius, so the diameter can be calculated as 2 * r = 2 * 2.01 = 4.02 inches.
So, the diameter of the circle with a circumference of 21.98 inches is 4.02 inches.
