By the concept of percentage there is 20% decrease in the number of people who went to the pool over these four weeks.
What is percentage?A percentage is a statistic or ratio that is expressed as a fraction of 100 in mathematics. But even though the abbreviation "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to signify it. A % is a dimensionless number; there is no specific unit of measurement for it. %, a relative figure signifying hundredths of any amount. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. A percentage is a figure or ratio that in mathematics represents a portion of one hundred. It is frequently represented by the sign "%" or just "percent" or "pct." For instance, the fraction or decimal 0.35 is comparable to 35%.
In July:
First week:
Number of people went to the local swimming pool
=1040
Second week:
110 fewer people went to the pool than in the first week
Number of people went to the local swimming pool
=1040 - 110
=930
Third week:
130 more people went to the pool than in the second week
Number of people went to the local swimming pool
=930 + 130
=1060
Fourth week:
228 fewer people went to the pool than in the third week
Number of people went to the local swimming pool
=1060 - 228
=832
Decrease in number of people over four week
= number of people in first week - number of people in fourth week
Decrease in number of people over four week
=1040 - 832
=208
Now, the percentage
= 20%
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Write a sine function that has an amplitude of 5, a midline of 4 and a period of 3/2
Note that in any sine function :
[tex]y=A\sin (B(x+C))+D[/tex]Amplitude = A
Verical Shift or midline = D
Period = (2π)/B
Horizontal or Phase Shift = C
From the given,
since we dont have any horizontal shift, C = 0.
Amplitude = 5, so A = 5
Midline = 4, so D = 4
and
Period = 3/2, so equating it to (2 π)/B
[tex]\frac{3}{2}=\frac{2\pi}{B}[/tex][tex]B=\frac{4\pi}{3}[/tex]Now, substituting the values obtained, the sine function will be :
[tex]y=5\sin (\frac{4\pi}{3}x)+4[/tex]Which statement describes the product of the expression 5 x 1/2?A, It is less than 1/2B. It is greater than %. C. It is between 5 and 6. D. It is between 1/2 and 5.
we have the expression
[tex]5\cdot\frac{1}{2}=\frac{5}{2}[/tex]so
Verify each statement
A, It is less than 1/2 -----> is not true
B. It is greater than 5 ----> is not true
C. It is between 5 and 6 ----> is not true
D. It is between 1/2 and 5 ----> is true
because
1/2 < 5/2 < 5
therefore
The answer is option D
what is 20/5*(3.8)=?
Given:
[tex]\frac{20}{5}\cdot3.8=\text{?}[/tex]first, we will find the result of dividing 20 by 5, then multiply the result by 3.8
so, the answer will be as follows:
[tex]\begin{gathered} \frac{20}{5}\cdot3.8 \\ \\ =4\cdot3.8=15.2 \end{gathered}[/tex]So, the answer will be 15.2
How do you solve an area of a rectangle with fractions
Given the figure, we can deduce the following information:
Perimeter = 65 in.
length = n
width = 11 2/4 in. = 23/2 in.
To determine the value of n, we use the formula:
[tex]P=2(l+w)[/tex]where:
P= Perimeter
l=length
w=width
We plug in what we know:
[tex]\begin{gathered} P=2(l+w) \\ 65=2(n+11\frac{2}{4}) \\ \text{Simplify and rearrange} \\ 65=2(n+\frac{23}{2}) \\ \frac{65}{2}=n+\frac{23}{2} \\ n=\frac{65}{2}-\frac{23}{2} \\ n=\frac{65-23}{2} \\ n=\frac{42}{2} \\ \text{Calculate} \\ n=21 \end{gathered}[/tex]Therefore, the value of n is 21 in.
A motivational speaker charges $5 for an adult's ticket and $2 for a child's ticket. For one event, he sold 785 tickets for $3280. How many adult tickets were sold? a) 785 b) 570 c) 215 d) 58
Answer:
the number of adult ticket sold is 570
[tex]x=570[/tex]Explanation:
Let x represent the number of adult ticket and y represent the number of child's ticket.
Given that he charges $5 for an adult's ticket and $2 for a child's ticket.
For one event, he sold 785 tickets.
So, we have;
[tex]x+y=785\text{ -----1}[/tex]he sold 785 tickets for $3280.
Then;
[tex]5x+2y=3280\text{ ------2}[/tex]let us solve by substitution.
make y the subject of formula in equation 1 and substitute to equation 2;
[tex]y=785-x[/tex]substituting to equation 2;
[tex]\begin{gathered} 5x+2y=3280 \\ 5x+2(785-x)=3280 \\ 5x+1570-2x=3280 \\ 5x-2x=3280-1570 \\ 3x=1710 \\ x=\frac{1710}{3} \\ x=570 \end{gathered}[/tex]Therefore, since x represent the number of adult tickets sold, then the number of adult ticket sold is 570
[tex]x=570[/tex]what is 6 3/8 written as a demcimal
Answer:
The solution is 6,375
Step-by-step explanation:
[tex] \sf 6 \frac{3}{8} \\ \\ = \sf \frac{6 \times 8 + 3}{8} \\ \\ \sf \frac{48 + 3}{8} \\ \\ = \sf \frac{51}{8} \\ \\ = \sf 51 \div 8 \\ \\ = \sf6.375[/tex]
sunscreen is priced at $10 per bottle, +8% tax. If Tonya purchases a bottle of sunscreen with a $20 bill, then what is her change
Solution
For this case we know that the price is 10$ per bottle with 8% of tax
We can find the tax using this:
[tex]\frac{10}{100}=\frac{x}{8}[/tex]With x= tax value, solving for x we got:
[tex]x=8\cdot\frac{10}{100}=0.8[/tex]Then the total price is: 10+0.8 = 10.8
Then we can find the change like this:
20-10.8= 9.2
fresh flowers charges $1.50 per flower and a $10 delivery fee. beautiful bouquets does not change a delivery fee but charges $4.00 per flower. which equation would allow you to find the number of flowers that would make the cost the same.1.50+ 10x=41.50x+10=41.50x + 10=4x1.50+ 10x=4
Step 1 : Let's review the information provided to us to answer the question correctly:
Fresh flower price = $ 1.50
Delivery = $ 10
Bouquets per flower = $ 4.00
Step 2:
Let x to represent the number of flowers, either fresh or in bouquet
Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.04 and a standard deviation of 1.53. Using the empirical rule, whatpercentage of American women have shoe sizes that are less than 11.1? Please do not round your answer.
The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution.
So we have
So we can apply the rule to obtain
A sample of 34 customers was taken at a local computer store. The customers were asked the prices of the computers they had bought. The data are summarized in the following table. Find the mean price for the sample. Round your answer to the nearest dollar
To find the mean we will sum the prices (total price, including repeated values) and divide by the total number of computers, then
[tex]m=\frac{14\cdot1400+11\cdot800+3\cdot2600+6\cdot1500}{34}[/tex]Using a calculator
[tex]\begin{gathered} m=\frac{45200}{34} \\ \end{gathered}[/tex]Do the division (use a calculator)
[tex]\begin{gathered} m=\frac{45200}{34} \\ \\ m=1329.41 \end{gathered}[/tex]The mean price is 1329.41
which domain restrictions apply to the rational expression? 14-2x / x^2-7x
The domain restrictions that apply on the given rational expression are that x can neither be 0 nor 7.
We are given the rational expression:-
[tex]\frac{(14-2x)}{(x^2-7x)}[/tex]
We have to find the domain restrictions that apply on the given expression.
We know that in a fraction, denominator cannot be 0, or else it will make the fraction indefinite.
Hence, by putting the denominator as 0, we will get the domain restrictions of the expression.
[tex]x^2-7x=0[/tex]
x(x - 7) = 0
x = 0 and 7
Hence, the domain restrictions that apply on the given rational expression are that x can neither be 0 nor 7.
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Jerry and Steve each had 24 candy bars to sell. Jerry sold 50% of his candy bars. Steve sold of his candy 6 bars. What fraction of the total candy bars did Jerry and Steve sell together?
Jerry and Steve each had 24 candy bars, that is, the total candy bars are 48:
If Jerry sold 50% of his candy bars, it means that he sold one half of the total, then, he sold 12 bars.
Steve sold 6 candy bars.
Then, they both sold 12 + 6 = 18 candy bars together.
The fraction of the total candy bars is then:
18/48 = 9/24 = 3/8
Please help!Which equation best represents the relationship between x and y in the graph?A. y = -3/4x - 3B. y = -4/3x - 3C. y = -3/4x - 4D. y = -4/3x - 4
Recall that the equation of a line in slope-intercept form is given by
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept of the line.
The y-intercept is the point where the line intersects the y-axis.
From the graph, we can see that the line intersects the y-axis at y = -3
So, the y-intercept is -3
The slope of the line is given by
[tex]m=\frac{\text{rise}}{\text{run}}=\frac{-3}{4}[/tex]The rise is the vertical distance between the two points on the line.
The run is the horizontal distance between the two points on the line.
So, the equation of the line is
[tex]y=-\frac{3}{4}x-3[/tex]Therefore, option A is the correct answer.
Tamara's monthly budget shows$490.00 in fixed expenses, $529.50in variable expenses, and anexpected income of $1,250.00.1. Why doesn't Tamara's budgetbalance?
She has an expected income of $1250.
The total expenses are $490 + $529.50 = $1019.50.
She has a superavit that she can save. This amount is $1250 - $1019.50 = $230.50.
Answer: the budget balance does not balance because the income is greater than the expenses.
During a class election the ratio of students who voted for candidate A compared tocandidate B was 7: 4. If candidate A received 21 votes, what is the combined amount ofvotes candidate A and candidate B received?
Given: Ratio of students that voted for A compared to B is 7:4
A recieved 21 votes so let B recieve x votes.
So as the given ratios,
[tex]\frac{7}{4}=\frac{21}{x}[/tex][tex]x=\frac{21\times4}{7}=12[/tex]Hence, combined votes received by candidate A and B is 12+21=33
in art class, Rafi made 5 clay bowls to send to family members. the bowls are fragile, so Rafi bought a roll of bubble wrap to protect them. he used a total of 11 feet of bubble wrap to wrap the bowls. how much bubble wrap did Rafi use for each bowl?
Number of bowls: 5
Bubble wrap = 11 feet
To find how many bubble wrap he used for each bowl, divide the bubble graph length by the number of bowls.
11 / 5 = 2.2
2.2 feet for each bowl
Which set of graphs can be used to find the solution to the equation?
Given
The inequality,
[tex]3e^x>-\frac{1}{2}x[/tex]To find:
Which set of graphs can be used to find the solution to the equation?
Explanation:
It is given that,
[tex]3e^x>-\frac{1}{2}x[/tex]That implies,
The graph representing 3e^x is,
Also, the graph representing y> - ( 1/2) x is,
By combining these two we get,
[tex]3e^x>-\frac{1}{2}x[/tex]using your place value vocabulary, describe the place value pattern you see occur in these four problems.10 × $8 = $8010 × $0.80 = 8.00$5.40 ÷ 10 = $0.54$0.60 ÷ 10 = $0.60
The place value of 8 on multiply by 10 becomes tens
The place value of the 8 in 0.80 by multiply with 10 becomes ones
Teh place of 5 on dividing with 10 becomes tenths
The place of 6 from 0.60 on divide by 10 becomes tenths
7(1 - 6p) need help please
Find 7•(1-6p)
First eliminate parenthesis
Apply distributive law
a•(b+c) = ab + ac
Then
7•(1-6p) = 7•1 - 7•6p
. = 7 -42p
ANSWER IS
7 - 42p
An archaeologist finds dinosaur bones 100 miles East and 200 miles North of his office. He finds whale bones 100 miles East and 300 miles South of his office. Graph and label these two points. How far apart are they?
Let's draw a picture of our problem:
where the red point (100 East, 200 Norh) represents the place where Archaeologist found the dinosaur. The blue point (100 East, 300 South) represents the place where Arcaeologist found the whale bones. Additionally, the green point (0,0) represents Arcaeologist's offfice.
Find the area, to the nearest thousandth, of the standard normal distribution between the given z-scores.z = 1 and z = 1.81
Since this is a normal distribution, the area between the z-scores z₁ = 1 and z₂ = 1.81 is just the probability that the random variable Z is between z₁ and z₂:
[tex]P(z_1\leq Z\leq z_2)=P(z_1\leq Z)-P(z_2\leq Z_{})=P(1\leq Z)-P(1.81\leq Z)[/tex]Using the values reported on tables for the standardized normal distribution, we know that:
[tex]\begin{gathered} P(1\leq Z)=0.158655 \\ P(1.81\leq Z)=0.035148 \end{gathered}[/tex]Now, using these results:
[tex]P(z_1\leq Z\leq z_2)=0.158655-0.035148=0.123507[/tex]Hello can you assist me please i need to solo e and Identity sine cosine or tangent and identify opposite hypnose or adjeact.Number 11.
Given the Right Triangle shown in the exercise, you need to use the following Trigonometric Function in order to find the measure of "x":
[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]In this case, you can identify that:
[tex]\begin{gathered} \alpha=21° \\ opposite=x \\ adjacent=18 \end{gathered}[/tex]Then, by substituting values and solving for "x", you get:
[tex]\begin{gathered} tan(21\text{\degree})=\frac{x}{18} \\ \\ 18\cdot tan(21\text{\degree})=x \end{gathered}[/tex][tex]x\approx6.9[/tex]Hence, the answer is:
[tex]x\approx6.9[/tex]The recycling center processed 36,000 pounds of recyclable materials. How many tons of recyclable materials are processed? A 18 TonC 72,000 TonB 38,000 TonD 180 Ton
We were told that the recycling center processed 36,000 pounds of recyclable materials. We would convert from pounds to tonnes. Recall,
1 tonne = 2000 pounds
Thus, x tonnes = 36000 pounds
By cross multiplying, we have
2000x = 36000
x = 36000/2000
x = 18
18 tons of recyclable materials were processed
in a popular restaurant on a Saturday night three out of every four customers are female. how many customers y are there for x number of total customers
Let y be the number of female customers in the restaurant. Since we know that 3 out of 4 customers are females and that x is the total number of customers, this means that:
[tex]y=\frac{3}{4}x[/tex]write the equation for each sentence below.a) (p) is the product of 7 to the sum of 3 and 9 b) The difference of (T) and 24 is 9 more than 34
(p) is the product of 7 to the sum of 3 and 9
This means we take the sum of "3" and "9" and multiply it with the variable "p". The expression is shown below
[tex]\begin{gathered} p\times(3+9) \\ =p\times12 \\ =12p \end{gathered}[/tex](b)The difference of (T) and 24 is 9 more than 34
The difference of T and 24 means T - 24
is 9 more than 34 means 34 + 9
Writing it together:
[tex]\begin{gathered} T-24=34+9 \\ T-24=43 \end{gathered}[/tex]A rectangular piece of metal is 25 in longer than it is wide Squares with sides 5 in long are cut from the four corners and the flaps are folded upward to form an openbox. If the volume of the box is 1530 in. What were the original dimensions of the piece of metal?What is the original width? ____in
Given:-
A rectangular piece of metal is 25 in longer than it is wide Squares with sides 5 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 1530 in.
To find the original width.
The formula for volume of the box is,
[tex]v=l\times b\times h[/tex]The volume given is 1530.
Also we have,
[tex]L=W+25,H=5[/tex]Substiutiting the values. we get,
[tex]\left(W+15\right)*W-10*5=1530[/tex]Divide both sides by 5,
[tex]\left(W+15\right)*W-10=306[/tex]So,
[tex]w^2+5w-150=306[/tex]So now we get,
[tex]w^2+5w-456=0[/tex]Now we solve the quadratic equation,
[tex]\begin{gathered} w=\frac{-5\pm\sqrt{5^2-4\cdot\:1\cdot\left(-456\right)}}{2\cdot\:1} \\ w=\frac{-5\pm\:43}{2\cdot\:1} \\ w=19,-24 \end{gathered}[/tex]So now we skip the negative value and take the positve value 19.
So the required value is 19.
A bag of 11 marbles contains 7 marbles with red on them, 6 with blue on them, 6 with green on them, and 3 with red and green on them. What is the probability that a randomly chosen marble has either green or red on it? Note that these events are not mutually exclusive. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
In the case of two not mutually exclusive events, we have that, given events A and B,
[tex]P(A\lor B)=P(A)+P(B)-P(A\cap B)[/tex]Notice that if we only include the first two contributions, we would count the intersection of the two events twice; therefore, we must subtract the probability of its intersection once.
In our case,
[tex]P(R\lor G)=\frac{7}{11}+\frac{6}{11}-\frac{3}{11}=\frac{10}{11}[/tex]Therefore, the answer is 10/11.
Find WX.Write your answer as an integer or as a decimal rounded to the nearest tenth.WX = ____
The give figure is of a triangle WXY right angled at X.
From the figure, WY=10 and
Using trigonometric property in the triangle,
[tex]\cos \theta=\frac{\text{adjacent side}}{\text{hypotenuse}}[/tex][tex]\begin{gathered} \cos Find WX by solving the above equation.[tex]\begin{gathered} WX=10\times\cos 44^{\circ} \\ =7.2 \end{gathered}[/tex]Therefore, WX=7.2.
Type the correct answer in each box.In this figure, sin ZQOP=cos ZRand cosZROQ sin 2
From the given figure, we have:
[tex]\begin{gathered} \sinSimilarly,[tex]\begin{gathered} \cosMarco wants to take a taxi cab ride if the cost to ride is 7.00 with the cost per m is 0.25 per mile and mr. o can only spend 30 write linear inequality that model
Each ride has a fixed cost of 7 and a cost that increases proportionally to the distance travelled of 0.25 per mile. Therefore the total cost of the ride is:
[tex]\text{ cost(x)}=0.25\cdot x+7[/tex]Where "x" is the distance in miles. Marco can only spend 30 on his ride, therefore the cost must be less or equal to that value.
[tex]\begin{gathered} \text{ cost(x)}\leq30 \\ 0.25\cdot x+7\leq30 \end{gathered}[/tex]We can solve the linear equation by isolating the "x" variable on the left side.
[tex]\begin{gathered} 0.25\cdot x\leq30-7 \\ 0.25\cdot x\leq23 \\ x\leq\frac{23}{0.25} \\ x\leq92 \end{gathered}[/tex]Marco's travel must be shorter or equal to 92 miles.