10 adults
Explanation
Step 1
find the unit rate
[tex]\text{unit rate=}\frac{Number\text{ of Children}}{\text{Number of adults}}[/tex]Let
number of children=56
number of adults=7
replace,
[tex]\begin{gathered} \text{unit rate=}\frac{Number\text{ of Children}}{\text{Number of adults}}= \\ \text{unit rate=}\frac{56\text{ Children}}{7\text{ adults}} \\ \text{unit rate= 8 Children per adult} \end{gathered}[/tex]Step 2
Let x represents the adults needed for 74 children
find the unit rate:
[tex]\begin{gathered} \text{unit rate=}\frac{Number\text{ of Children}}{\text{Number of adults}} \\ \text{unit rate=}\frac{74}{x} \end{gathered}[/tex]as the unit rate must be the same
[tex]\begin{gathered} 8\frac{Children}{\text{adult}}=\frac{74}{x} \\ 8=\frac{74}{x} \\ cross\text{ multiply} \\ 8x=74\cdot1 \\ 8x=74 \\ \text{divide both sides by 8} \\ \frac{8x}{8}=\frac{74}{8} \\ x=9.25 \\ \text{hence, we n}eed\text{ 10 adults at the center} \end{gathered}[/tex]What postulate or theorem is used in the picture below?
If we have that in two triangles we have that the corresponding sides and the included angle are congruent, then we can say that both triangles are congruent. This is called the SAS (side-angle-side) postulate.
Then, in summary, the method that proves that both triangles are congruent is SAS (Side-Angle-Side) postulate (second option).
-x+2y=-158x-2y=-20After performing your first step in Elimination, what is the resulting equation?Then solve for x
Let:
[tex]\begin{gathered} -x+2y=-15_{\text{ }}(1) \\ 8x-2y=-20_{\text{ }}(2) \end{gathered}[/tex]Using elimination:
[tex]\begin{gathered} (1)+(2) \\ -x+8x+2y-2y=-15-20 \\ 7x=-35 \end{gathered}[/tex]Solve for x:
Divide both sides by 7:
[tex]\begin{gathered} \frac{7x}{7}=-\frac{35}{7} \\ x=-5 \end{gathered}[/tex]Replace the value of x into (1):
[tex]\begin{gathered} 5+2y=-15 \\ 2y=-20 \\ y=-\frac{20}{2} \\ y=-10 \end{gathered}[/tex]There are two types of tickets sold at the Canadian Formula One Grand Prix race. The price of 6 grandstand tickets and 4 general admission tickets is $3200. The price of 8 grandstand tickets and 8 general admission tickets is $4880. What is the price of each type of ticket?
Let:
x = price of the grandstand ticket
y = price of the general admission ticket
The price of 6 grandstand tickets and 4 general admission tickets is $3200, so:
[tex]6x+4y=3200[/tex]The price of 8 grandstand tickets and 8 general admission tickets is $4880, so:
[tex]8x+8y=4880[/tex]Let:
[tex]\begin{gathered} 6x+4y=3200_{\text{ }}(1) \\ 8x+8y=4880_{\text{ }}(2) \end{gathered}[/tex]Using elimination method:
[tex]\begin{gathered} 2(1)-(2)\colon_{} \\ 12x-8x+8y-8y=6400-4880 \\ 4x=1520 \\ x=\frac{1520}{4} \\ x=380 \end{gathered}[/tex]replace the value of x into (1):
[tex]\begin{gathered} 6(380)+4y=3200 \\ 2280+4y=3200 \\ 4y=3200-2280 \\ 4y=920 \\ y=\frac{920}{4} \\ y=230 \end{gathered}[/tex]The price of the grandstand ticket is $380 and the price of the general admission ticket is $230
. A pie company made 57 apple pies and 38 cherry pies each day for 14 days. How many apples pies does the company make in all?
To determine the total number of apples pies done, multiply the number of apple pies done each day by 14:
[tex]57\cdot14=798[/tex]Hence, the company made a total of 798 apple pies.
Manuel used pattern blocks to build the shapes below. The block marked A is a square, B is a trapezoid, C is a rhombus (aparallelogram with equal sides), and D is a triangle. Find the area of each of Manuel's shapes.
Solving for area of first figure
Recall the following formula for area of 2D figures
[tex]\begin{gathered} A_{\text{square}}=s^2 \\ A_{\text{trapezoid}}=\frac{a+b}{2}h \end{gathered}[/tex]The first figure consist of 2 figures with a square of side length of 2.5 cm, and a trapezoid with length 2.5 cm for the upper base, 5 cm for the lower base, and 2 cm for the height.
Calculate the area by getting the sum of the areas of the two figures
[tex]\begin{gathered} \text{Square: }s=2.5\text{ cm} \\ \text{Trapezoid: }a=2.5\text{ cm},b=5\text{ cm},h=2\text{ cm} \\ \\ A=s^2+\frac{a+b}{2}h \\ A=(2.5\text{ cm})^2+\frac{2.5\text{ cm}+5\text{ cm}}{2}\cdot2 \\ A=6.25\text{ cm}^2+\frac{7.5\text{ cm}}{\cancel{2}}\cdot\cancel{2}\text{ cm} \\ A=13.75\text{ cm}^2 \end{gathered}[/tex]The area of the first figure therefore is 13.75 square centimeters.
Solving for the area of the second figure
Recall the following areas for 2D figures
[tex]\begin{gathered} A_{\text{triangle}}=\frac{1}{2}bh \\ A_{\text{rhombus}}=bh \end{gathered}[/tex]Using the same procedures as above, we get the following
[tex]\begin{gathered} \text{Triangle: }b=2.5\text{ cm},h=2.2\text{ cm} \\ \text{Rhombus: }b=2.5\text{ cm},h=2\text{ cm} \\ \\ A=\frac{1}{2}(2.5\text{ cm})(2.2\text{ cm})+(2.5\text{ cm})(2\text{ cm}) \\ A=\frac{1}{2}(5.5\text{ cm}^2)+5\text{ cm}^2 \\ A=2.75\text{ cm}^2+5\text{ cm}^2 \\ A=7.75\text{ cm}^2 \end{gathered}[/tex]Therefore, the area of the second figure is 7.75 square centimeters.
The sales tax rate is 10%. If Lindsey buys a fountain priced at $125.40, how much tax will she Inay? $
We have to calculate the sales tax over a purchase of $125.40.
The sales tax rate is 10%, so we can calculate:
[tex]\text{Sales tax}=\frac{10}{100}\cdot125.40=0.1\cdot125.40=12.54[/tex]Answer: the sales tax on this purchase is $12.54,
What is the slope of the line given by the following equation? 13x + 4y = 52
Given the linear equation;
[tex]13x+4y=52-----1[/tex]We can find the slope by comparing the above equation with the general equation of a line. This can be seen below.
[tex]y=mx+c------2[/tex]Where m is the slope of the equation
We then make y the subject of the formula in equation one
[tex]\begin{gathered} 13x+4y=52 \\ \text{subtract 13x from both sides} \\ 13x-13x+4y=52-13x \\ 4y=52-13x \\ \text{Divide both sides by 4} \\ \frac{4y}{4}=\frac{52}{4}-\frac{13x}{4} \\ y=13-\frac{13x}{4} \end{gathered}[/tex]By comparison,
[tex]m=-\frac{13}{4}[/tex]Answer: The slope of the equation is
[tex]\text{slope}=-\frac{13}{4}[/tex]if pa =1/3 and pb =2/5 and p(ab) = 3/5 what is p(ab)
Given:
[tex]P(A)=\frac{1}{3}\text{ ; P(B)=}\frac{2}{5}\text{ ; P(A}\cup B)=\frac{3}{5}[/tex][tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex][tex]\begin{gathered} \frac{3}{5}=\frac{1}{3}+\frac{2}{5}-P(A\cap B) \\ P(A\cap B)=\frac{1}{3}+\frac{2}{5}-\frac{3}{5} \\ P(A\cap B)=\frac{5+6-9}{15} \\ P(A\cap B)=\frac{2}{15} \end{gathered}[/tex]Option D is the final answer.
Hugo is serving fruit sorbet at his party He has 1 gallon of fruit sorbet to serve to 32 friends. If each person receives the same amount, how many cups of fruit sorbet will each person get? A. 1/4 cupB.1/2 cupC. 3/4 cupD. 1 cup
Since 1 gallon is equal to 16 cups, each person will get
[tex]\begin{gathered} \frac{16}{32}\text{ cup} \\ \frac{16}{32}=\frac{1}{2} \\ \\ \text{ each person will get } \\ \frac{1}{2}\text{ cup} \end{gathered}[/tex]A company purchased 10,000 pairs of men's slacks for $18.86 per pair and marked them up $22.63. What was the selling price of each pair of slacks? Use the formula S=C+M
Problem:
A company purchased 10,000 pairs of men's slacks for $18.86 per pair and marked them up $22.63. What was the selling price of each pair of slacks? Use the formula S=C+M.
Solution:
Cost = $18.86
Markup = $22.63
Markup = Sell Price - Cost
Sell Price = Cost + Markup
Sell Price = 18.86+ 22.63
Sell Price = $41.49
The selling price of each pair of slacks was $41.49.
Find the length of an arc of a circle whose central angle is 212º and radius is 5.3 inches.Round your answer to the nearest tenth.
The formula for the arc length is,
[tex]L=2\pi r\cdot\frac{\theta}{360}[/tex]Substitute the values in the formula to determine the arc length.
[tex]\begin{gathered} L=2\pi\cdot5.3\cdot\frac{212}{360} \\ =19.61 \\ \approx19.6 \end{gathered}[/tex]So answer is 19.6 inches.
What is the best approximation for the area of a semi-circle with a diameter of 11.8 ( Use 3.14 for pie
Answer:
54.7units^2
Explanation:
Area of a semi-circle = \pid^2/8
d is the diameter of the semi circle
Given d = 11.8
Area = 3.14(11.8)^2/8
Area of the semi circle = 3.14(139.24)/8
Area of the semi circle = 437.2136/8
Area of the semi circle = 54.6517units^2
Hence the best approximation is 54.7units^2
The citizens of a certain community were asked to choose their favorite pet. The pie chart below shows the distribution of the citizens answers. If there are 90,000 citizens in the community, how many chose hamsters, fish, snakes?
ANSWER :
27000
EXPLANATION :
From the problem, 7% chose hamsters, 15% chose Fish and 8% chose Snakes.
A total of 7 + 15 + 8 = 30%
Multiply this percentage by the population (90,000) to get the number of people who chose these pets.
That will be :
[tex]90000(0.30)=27000[/tex]A trap for insects is in the shape of a triangular prism. The area of the base is 4.5 in2 and the height of the prism is 3 in. What is the volume of this trap? The volume of the trap is in3
Answer:
[tex]\text{Volume}=13.5in^3[/tex]Step-by-step explanation:
The area of the volume is represented by the multiplication of the area of the base by the height:
[tex]\text{Volume}=\text{Area}\cdot\text{height}[/tex]Then, the volume of the trap is:
[tex]\begin{gathered} \text{Volume}=4.5\cdot3 \\ \text{Volume}=13.5in^3 \end{gathered}[/tex]Solve the following equation for and y - 3 - 7i + 6x = 19 + 2i + 13yi
Okay, here we have this:
Considering the provided equation, we are going to solve it, so we obtain the following:
[tex]\begin{gathered} -3-7i+6x=19+2i+13yi \\ (-3+6x)-7i=19+(2+13y)i \end{gathered}[/tex]So let's remember that a set of complex numbers can only be equal if their real and imaginary parts are equal. According to this we have:
-3+6x=19, -7=2+13y
6x=19+3, -7-2=13y
6x=22, -9=13y
x=22/6, y=-9/13
x=11/3, y=-9/13
Finally we obtain the following set: x=11/3, y=-9/13.
16. An empty jar has a volume of8x2 + 2x - 4 cubic inches. Josh pours4x2 – 3x +2 cubic inches of waterinto the jar. How many more cubicinches of water could the jar stillhold?
Volume of empty jar 8x² + 2x - 4
Volume of water poured = 4x² - 3x + 2
More number of cubic inches that the jar can still hold= (8x² +2x - 4) -(4x²- 3x+2)
= 8x² + 2x - 4 - 4x² + 3x - 2
Rearrange
=8x² - 4x² + 2x + 3x - 4 - 2
=4x² + 5x - 6
Hence, the more number of cubic inches that the jar can still hold is
4x² + 5x - 6
11.y +9=-3(x-2)14.y- 6= 4( x+3)17.y-2 =-1/2(x-4)
Three linear equations , write in standard form
y +9= 3*(x+2)
y = 3x + 3 -9 = 3x -6
y-6= 4(x + 3)
y = 4x +12 -6= 4x + 6
y - 2 = -1/2(x-4)
y = (-1/2)x +2 +2= (-1/2)x +4
a single lily pad lies on the surface of a pond. Each day the number of lily pads doubles until the entire pond is covered on day 30. make a table that shows the number of lily pads at each day rfom day 1 to day 5. let x be the day number and y be the number of lily ad on that day
Given:
A single lily pad lies on the surface of a pond.
The number of lily pads doubles each day until the entire pond is covered on day 30.
To make a table that shows the number of lily pads on each day from day 1 to day 5:
Let x be the day number and y be the number of lily ads on that day.
On the first day, the number of lilies is 1.
On the second day, the number of Lillies is 2.
On the third day, the number of Lillies is 4.
And so on.
So, the table is,
r(x)=−x−7 when x=−2,0, and 5
Given,
The expression of the function,
[tex]r(x)=-x-7[/tex]The value of r(x) at x = -2 is,
[tex]r(-2)=-(-2)-7=2-7=-5[/tex]The value of r(x) at x = 0 is,
[tex]r(0)=-(0)-7=0-7=-7[/tex]The value of r(x) at x = 5 is,
[tex]r(5)=-(5)-7=-5-7=-12[/tex]Hence, the value of r(x) is -2, -7 and -12.
is 88∘ more than the smaller angle. Find the measure of the larger angle.
Let
x -----> large angle
y ----> smaller angle
so
Remember that
If two angles are supplementary, then their sum is equal to 180 degrees
so
x+y=180
y=180-x ------> equation A
and
x=y+88
y=x-88 -----> equation B
equate both equations
180-x=x-88
x+x=180+88
2x=268
x=134 degrees
the answer is 134 degreesCan you please check number 4 and check parts a, b, and c to make sure it’s right please
if the scale in the drawing is 1 centimeter= 20 meters, then:
a) Playground 3 centimeters.
[tex]\begin{gathered} \frac{1cm}{20m}=\text{ }\frac{3cm}{x}= \\ \text{ x\lparen1cm\rparen=\lparen20m\rparen\lparen3cm\rparen} \\ x=\text{ 60 meters} \end{gathered}[/tex]b) Tennis courts= 5.2cm
[tex]\begin{gathered} \frac{1cm}{20m}=\text{ }\frac{5.2cm}{x} \\ x(1cm)=\text{ \lparen5.2cm\rparen\lparen20m\rparen} \\ x=\text{ 104 meters} \end{gathered}[/tex]c) Walking trail= 21.7 cm
[tex]\begin{gathered} \frac{1cm}{20m}=\frac{21.7cm}{x} \\ \\ x(1cm)=(21.7cm)(20m) \\ x=\text{ 434 meters} \end{gathered}[/tex]Select the appropriate graph for each inequality.1. {x|x<-3}a.<用HHHHH>-10 -1 -8 -7 -6 - 4 -3 -2 -1 01 23 4 5 6 7 8 9 10
Given the inequality x| x< -3
The graph of the inequality will be as following :
Question 7Find the slope of the line that goes through the given points.(-1, 7).(-8, 7)1092
Given:
There are given that the two points;
[tex](-1,7)\text{ and (-8,7)}[/tex]Explanation:
To find the slope of the line from the given point, we need to use the slope formula:
So,
From the formula of the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]x_1=-1,y_1=7,x_2=-8,y_2=7_{}[/tex]Then,
Put all the above values into the given formula:;
So,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{7_{}-7_{}}{-8_{}-(-1)_{}} \end{gathered}[/tex]Then,
[tex]\begin{gathered} m=\frac{7_{}-7_{}}{-8_{}+1_{}} \\ m=\frac{0}{-7} \\ m=0 \end{gathered}[/tex]Final answer:
The slope of the given line is 0.
Hence, the correct option is B (0)
The accompanying table shows the value of a car over time that was purchased for 13700 dollars, where x is years and y is the value of the car in dollars Write an exponential regression equation for this set of data, rounding all coefficients to the nearest thousandth . Using this equation , determine the value of the car, to the nearest cent , after 12 years ,
ANSWER
[tex]y=13700(0.919)^x[/tex]Value of the car after 12 year: $4971.72
EXPLANATION
The exponential regression equation is
[tex]y=ab^x[/tex]Using the values of the table we can find both a and b. Note that a is the value of y when x = 0, so a = 13700.
For b replace a, and x and y with the next values of the table:
[tex]\begin{gathered} 12590=13700b^1 \\ b=\frac{12590}{13700} \\ b\approx0.919 \end{gathered}[/tex]The equation is
[tex]y=13700(0.919)^x[/tex]To find the value of the car after 12 years, replace x = 12:
[tex]y=13700(0.919)^{12}\approx4971.72[/tex]BD bisects ABC. Ifm ABD - 3x +27 andm2DBC = 8x-33, what ism2 DBC?
because the line BC bisects the angle ABC we can do the next equality
the angles DBC and ABD are equals
angle ABD = angle DBC
the value of ABD = 3x+37
the value of DBC = 8x-33
then we can do the next equality with the values
3x+27=8x-33
we need to clear x, so the terms of x will go to the right side and the terms without x will go to the left side
27+33=8x-3x
60=5x
we can change the sides in order to have x
5x=60
x=60/5
x=12
angle DBC=8(12)-33=63
the angle DBC is 63°
Find a linear inequality for the graph.y ≥ 3y > 3x ≤ 3x < 3
Given:
A graph is given
Required:
To tell whose inequality is this.
Explanation:
[tex]\begin{gathered} This\text{ graph shows the inequality of } \\ y\ge3 \end{gathered}[/tex]Required answer:
Option A is correct.
A person wants to increase a (5 in. x 7 in.) photo to an (8 in. x 10 in.) but since the aspect ratios are not the same some of the picture will get chopped off. ti 8" original picture blown-up picture with frame shown What percentage of the picture can be used in the (8 in. x 10 in.) frame?
Using the properties of aspect ratio we calculate that approximately 89.3% of the picture will be used in the new frame.
The original picture has the dimension 5 × 7 inches .
The new dimension is 8 by 10.
Now let us consider that the height is 8 inches but the width will be x for the increased size picture.
Now we will us ratio to find the width.
original / new = 5/8 = 7 / x
or, x = 11.2 inches.
Area of the new picture = 11.2 × 8 = 89.6 square inches.
Area of the picture frame = 8 × 10 = 80 square inches.
Percentage of picture used
= 80 /89.6 × 100 %
= 89.268...
≈ 89.3%
Therefore using the properties of aspect ratio we calculate that approximately 89.3% of the picture will be used in the new frame.
to learn more about aspect ratio visit:
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It is reported that approximately 20 squaremiles of dry land and wetland were convertedto water along the Atlantic coast between 1996and 2011. A small unpopulated island in the AtlanticOcean is 2000 ft wide by 9,380 feet long. Atthis rate, how long before the island issubmerged?
2 months
1) Notice that the sinking rate is 20miles² per 5 years (2011-1996) so:
[tex]\frac{20}{5}=\frac{4m^2}{y}[/tex]So the rate is 4 square miles per year.
2) We need to convert those measures from feet to miles:
[tex]\begin{gathered} 1\text{ mile=5280ft} \\ 2000ft=\frac{2000}{5280}=0.378miles \\ 9380ft=\frac{9380}{5280}=1.7765miles \end{gathered}[/tex]So, now let's find the area multiplying the width by the height:
[tex]\begin{gathered} A=1.7765\cdot0.378 \\ A=0.671517m^2 \end{gathered}[/tex]Now, considering the sinking rate of 4miles²/year we can write the following pair of ratios:
[tex]\begin{gathered} 1year-------4miles^2 \\ x----------0.6715 \\ 4x=0.6715 \\ \frac{4x}{4}=\frac{0.6715}{4} \\ x=0.17 \\ \\ --- \\ 0.17\times12\approx2 \end{gathered}[/tex]Note that we found that approximately 0.17 year is necessary to submerge tat island, converting that to months, we can state that in approximately 2 months
If point (x, y) is rotated 270 degrees about the origin, the resulting point is (y, -x).TrueFalse
When we perform a clockwise rotation of 270° about the origin of a point (x, y) the resulting point is (-y, x), then the answer is false. But if the rotation is counterclockwise, the resulting point is (y, -x), so the answer is true
How many different combinations of nine different carrots can be chosen from a bag of 20? O 125,970 O 167,960
We have a bag of 20 carrots, all different, and we have to calculate the possible combinations in groups of 9 carrots.
We can calculate this with the formula for combinations (as the order does not matter):
[tex]_{20}C_9=\binom{20}{9}=\frac{20!}{9!(20-9)!}=\frac{20!}{9!11!}=167960[/tex]Answer: there are 167,960 possible combinatios