ANSWER
27 balls
EXPLANATION
The points scored by the other team are the number of balls Diana and Becky didn't stop.
We know that if the other team would make 10 attempts of goal, only 1 would result in a point. The ratio of scored points to stopped balls is 1:9
Let x be the number of balls they stopped in this match. The other team scored 3 points, so the ratio is 3:x. We know that the ratio should be constant, which means,
[tex]\frac{1}{9}=\frac{3}{x}[/tex]To solve this, we have to multiply both sides by x. On the right side, the x cancels out,
[tex]\begin{gathered} \frac{1}{9}x=\frac{3x}{x} \\ \frac{1}{9}x=3 \end{gathered}[/tex]And then multiply both sides by 9,
[tex]\begin{gathered} \frac{1}{9}\cdot9x=3\cdot9 \\ x=27 \end{gathered}[/tex]Hence, Diana and Becky stopped 27 balls.
Nina deposited $20.59 in her checking account. Later that week, she wrote a checkfor one-third the amount in the account, and then another check for $9.74. If shehad $108.60 left in her account, how much did she have to begin with.
1) Reading carefully, we can do it step by step.
2) She had deposited $20.59 and wrote a check, since she wrote a check we can understand that as a debit so we can write out the following:
[tex]\begin{gathered} 20.59-\frac{20.59}{3}= \\ 20.59-6.86 \\ 13.7 \end{gathered}[/tex]Note that we rounded off to the nearest hundredth.
2.2) So now, she wrote another check, i.e. -$9.74
[tex]\begin{gathered} \$13.7-\$9.74 \\ \$4 \\ 108.60 \\ 108.60+\mleft(20.59-6.86-9.74\mright)=112.59 \end{gathered}[/tex]Which functions are inverses of each other?a. Both Pair 1 and Pair 2b. Pair 1 onlyc. Pair 2 onlyd. neither Pair 1 nor Pair 2
Solution
For pair 1
[tex]\begin{gathered} f(x)=2x-6,g(x)=\frac{x}{2}+3 \\ \mathrm{A\: function\: g\: is\: the\: inverse\: of\: function\: f\: if\: for}\: y=f\mleft(x\mright),\: \: x=g\mleft(y\mright)\: \end{gathered}[/tex][tex]\begin{gathered} f(x)=2x-6 \\ f(x)=y \\ y=2x-6 \\ x=2y-6 \\ x+6=2y \\ \text{divide both side by 2} \\ \frac{x+6}{2}=\frac{2y}{2}_{} \\ y=\frac{x}{2}+3 \end{gathered}[/tex]They are inverse of each other
For pair 2
[tex]\begin{gathered} f(x)=7x,g(x)=-7x \\ \text{Inverse of f(x) = x/7} \end{gathered}[/tex][tex]\begin{gathered} f(x)=7x \\ y=7x \\ x=7y \\ y=\frac{x}{7} \end{gathered}[/tex]They are not inverse of each other
Therefore only pair 1 are inverse of each other
Hence the correct answer is Option B
Jan is trying to fix her circular window and needs to know how much space it takes up. It has a diameter of 10 inches.
ANSWER
The area is 78.54 in²
EXPLANATION
We need to find the area of this circle. The area of a circle with radius r is:
[tex]A=\pi r^2[/tex]The diameter of a circle is twice the radius, so if the diameter is 10 inches, then the radius is 5 inches:
[tex]A=\pi\cdot5^2=25\pi=78.54in^2[/tex]This answer is rounded to the nearest hundredth.
Write the equation 4x + 8y = -24 in slope-intercept form. Then graph the equation. O None of the other answers are correct
4x + 8y = - 24
8y = -4x - 24
divide both sides by 8
y = -1/2x - 3
[tex]y\text{ = }\frac{-1}{2}x\text{ - 3}[/tex]Using y = mx + c
To obtain y intercept, make x = 0
so y = -1/2(0) -3
y = -3
(0,-3)
To obtain x intercept, make y = 0
so that 0 = -1/2x -3
1/2x = -3
x = -6
(-6,0)
Taking the points (0,-3) and (-6,0) to plot the graph
Hi I need help with a couple of questions. It's math algebra
The equation above is the formula of the speed (s) in terms of the distance (d) and the time (t).
For the distance 132 mi
With a speed of 8 miles per hour it takes the next hours:
[tex]\begin{gathered} \\ \text{Solve t:} \\ s\cdot t=d \\ t=\frac{d}{s} \\ \\ t=\frac{132mi}{8\frac{mi}{h}}=16.5h \end{gathered}[/tex]With a speed of 12 miles per hour it takes the next hours:
[tex]t=\frac{132mi}{12\frac{mi}{h}}=11h[/tex]Then, the possible number of hours that take to the kayaker to travel 132 miles is between 11 and 16.5
List all possible rational zeros for the function. (Enter your answers as a comma-separated list.)f(x) = 2x3 + 3x2 − 8x + 5
We will list all the possible rational zeros for the polynomial
[tex]f(x)=2x^3+3x^2-8x+5[/tex]to find it we will apply the Rational root theorem. It states that each rational zero(s) of a polynomial with integers coefficients is of the form
[tex]\frac{p}{q}[/tex]where:
* p is a factor of the coefficient of the zero order term in the polynomial ( in our case this coefficient is 5)
* q is a factor of the leading coefficient , that is the coefficient that multiply the variable to the biggest power (in our case that coefficient is 2)
* p and q are relative primes, that is , they does not have common factors.
Finding the possibilities for rational roots:
Just summarizing the information until now, we have:
[tex]p=5\text{ and q=2}[/tex]
we also have that:
[tex]factors\text{ of 5= \textbraceleft1,5,-1,-5\textbraceright}[/tex]and
[tex]factors\text{ of 2 = \textbraceleft1,-1,2,-2\textbraceright}[/tex]So, on the right of the equations above, we have all the possible values that can take p and q, respectively. It only rests to construct all the possibilities, we do
For the function N(t) = 4t + 5] + 3. evaluate N(2).
Answer:
Explanation:
Putting in x = 2 in the function gives
[tex]N(2)=4|2+5|+3[/tex][tex]N(2)=31[/tex]which is our answer!
i just need a tutor to tell me if my answers are correct or wrong
Given the expression below,
I don’t know if I’m right I need to know
ANSWER
[tex]x=3[/tex]EXPLANATION
We want to identify the positive solution to the graph.
The solutions to a quadratic graph are the points where the graph touches the x-axis on the coordinate plane. The positive solution to the graph is the point where the graph touches the positive x-axis.
Hence, the positive solution to the given graph is x = 3.
Find the value of 2[3(x2 – 5) + 5y] when x = 9 and y = 3.
Answer
The value of the expression is 486
Step-by-step explanation
Given the expression
2[3(x^2 - 5) + 5y]
To solve this, we will be applying the PEMDAS rule
Where x = 9 and y = 3
Step 1: solve the smaller parenthesis first
2[3(9^2 - 5) + 5*3]
2 [ 3(81 - 5) + 15]
2 [ 3(76) + 15]
2 [ 228 + 15]
Solve the larger parenthesis
2 [ 243] = 486
Hence, the value of the expression is 486
the circle graph shown above represents the distribution of the grades of 40 students in a certain geometry class. How many students received Bs or Cs?
Given:
Total number of students = 40
From the circle graph given, let's determine the number of students that received Bs or Cs.
Given:
Percentage of students that received Bs = 30%
Percentage of students that received Cs = 40%
Percentage of student that received Bs or Cs = 40% + 30% = 70%
Thus, to find the number of students who received Bs or Cs, we have the equation below:
No of students who received Bs or Cs = (% of students who received Bs or Cs) x (Total n0 of students)
[tex]\text{ No of student who received Bs or Cs = 70\% of 40}[/tex]Thus, we have:
[tex]\begin{gathered} \text{ No of students who received Bs or Cs = }\frac{70}{100}\ast40 \\ \\ =0.70\ast40 \\ \\ =28 \end{gathered}[/tex]Therefore, the number of students who received Bs or Cs are 28
ANSWER:
C. 28
If 12(5r + 6t) = x, then in terms of w, what is 48(30r + 361)?
w=12(5r+6t)
Using distributive property:
w=60r+72t
and
48(30r+36t)=1440r+1728t
Now, let's multiply both sides of w=60r+72t by 24:
24*w=24*(60r+72t)
Using distributive property again:
24w=1440r+1728t
Therefore, 48(30r + 361) is equal to 24w.
Needed help to catch up before summer come any help will be good thank you
We have the following set of inequations
[tex]\begin{cases}y-2<-5{} \\ y-2>{5}\end{cases}[/tex]Let's solve both for y, it will give us
[tex]\begin{cases}y<-5{+2} \\ y>{5}+2\end{cases}\Rightarrow\begin{cases}y<-3 \\ y>7\end{cases}[/tex]Therefore y must be smaller than -3 and bigger than 7, then, the set between -3 and 7 is not part of the solution. the solution in fact is
[tex]S=(-\infty,-3)\cup(7,+\infty)[/tex]Let's do it in the graph!
The solution to the inequations is in blue on the graph.
Find the coordinates of point Q that lies along the directed line segment from R(-2, 4) to S(18, -6) and partitions the segment in the ratio of 3:7.A. (4, 1)B. (16, -2)C. (6, -3)D. (8, -1)
The coordinates of the point which partitions a directed line segment AB at the ratio a:b from A(x1, y1) to B(x2, y2) is computed as follows:
[tex](x,y)=(x_1+\frac{a}{a+b}(x_2-x_1),y_1+\frac{a}{a+b}(y_2-y_1_{}))[/tex]In this case, the segment goes from R(-2, 4) to S(18, -6), and the partition ratio is 3:7. Substituting into the above formula, we get:
[tex]\begin{gathered} (x,y)=(-2+\frac{3}{3+7}(18-(-2)),4+\frac{3}{3+7}(-6-4)) \\ (x,y)=(-2+\frac{3}{10}\cdot20,4+\frac{3}{10}(-10)) \\ (x,y)=(4,1) \end{gathered}[/tex]Fill out the blank to make the given table a probability distribution.
Answer:
[tex]0.06[/tex]Explanation:
Here, we want to fill out the blank
For us to have a probability distribution, the sum of the individual probabilities should be one
Mathematically, for us to get the value of the blank, we have to subtract the sum of the probabilities from 1. This is because the value of the area under the probability distribution is 1 square unit
Thus,we have it that:
[tex]\begin{gathered} P(-1)\text{ = 1 - (0.11 + 0.25 + 0.36 + 0.18 + 0.04)} \\ P(-1)\text{ = 0.06} \end{gathered}[/tex]for a school science project, john noted the temperature at the same time every day for 1 week the high temperature for the week was 27 Fahrenheit and the low temperature for the week was -3 Fahrenheit what is the difference between the high and low temperatures down recorded
To answer the question we shall use a number line that begins with zero and moves in the right direction for positive values and then towards the left direction for negative values.
The high temperature recorded was 27 (positive). The low temperature was -3 (negative). The difference therefore is, 30. That is 27 to the right and from zero to the left, 3, altogether the difference is 30 on the number line.
This can better yet be expressed as follows;
[tex]\begin{gathered} \text{Difference}=27-\lbrack-3\rbrack \\ \text{Difference}=27+3 \\ \text{Difference}=30 \end{gathered}[/tex]The table shows conversions of common units of capacity.Units of CapacityCustomary System UnitsMetric System Units1 gallon3.79 liters1 quart0.95 liters1 pint0.473 liters1 cup0.237 litersApproximately how many centiliters are in 3 quarts? Round answer to the nearest unit.
Given data:
The value o 1 quart is 1 quart=0.95 liters.
Multiply the above expression with 3 on both sides.
3(1 quart)=3(0.95 liters)
3 quarts =2.
13.3x + 8.1 = 74.6 solve for x
Answer:
x = 5
Step-by-step explanation:
1) Get rid of the 8.1
Whenever you are given a question like this you have to try get rid of any other numbers on the side with the x that don't include the x.
We can see that we can first get rid of the 8.1 to do this we have to subtract 8.1 from both sides.
13.3x + 8.1 -8.1 = 13.3x
74.6 - 8.1 =66.5
2) Isolate the x
To get our final value of x you have to divide both sides from 13.3! This is because we were previously left with 13.3x = 66.5 and we can see that you have to multiply 13.3 by x to get 66.5, in return to find x you should have to do the inverse.
66.5 ÷ 13.3 = 5
HINT:
For every question like this you have to do the inverse of whatever you are given. For example, we had to take away 8.1 because in the question it says add!
Hope this helps, have a great day!
in a recent survey, 60% of the community favored building a health center in their neighborhood. If 14 citizens are chosen, find the probability that exactly 11 of them favor the building of the health center. Round to the nearest thousandth.
Answer:
0.085
Explanation:
To find the probability, we will use the binomial distribution because there are n identical events ( 14 citizens), with a probability of success (p = 60%). Then, the probability can be calculated as:
[tex]P(x)=\text{nCx}\cdot p^x\cdot(1-p)^{n-x}[/tex]Where nCx is equal to
[tex]\text{nCx}=\frac{n!}{x!(n-x)!}[/tex]So, to find the probability that exactly 11 of them favor the building of the health center, we need to replace x = 11, n = 14, and p = 0.6
[tex]14C11=\frac{14!}{11!(14-11)!}=\frac{14!}{11!(3!)}=364[/tex][tex]\begin{gathered} P(11)=364(0.6)^{11}(1-0.6)^{14-11} \\ P(11)=0.085 \end{gathered}[/tex]Therefore, the probability that exactly 11 of them favor the building of the health center is 0.085
factor as the product of two binomial x^2+3x+2= _____
We are given the trinomial
[tex]x^2+3x+2[/tex]We can factor it as the product two binomials as
[tex](x+a)(x+b)[/tex]Where
a and b are two numbers that has
• a product of 2
,• a sum of 3
So, which two numbers multiplied gives us "2" and added gives us "3"?
It is "+2" and "+1".
Thus, we can factor the trinomial as:
[tex]\begin{gathered} x^2+3x+2 \\ =(x+2)(x+1) \end{gathered}[/tex]are the triangles similar? if so what is the scale factor?
a) Yes, The scale factor is 3/2
Explanation
Step 1
to check if the triangles are similar, we need to prove that the ratios of the longest side and one sideof the triangle are similar
so
let
[tex]ratio=\frac{longest\text{ side}}{side}[/tex]hence
[tex]\begin{gathered} ratio_1=\frac{8}{5}=1.6 \\ ratio_2=\frac{12}{7.5}=1.6 \end{gathered}[/tex]therefore, the triangles are similar
Step 2
now, to find the scale factor we use the formula
[tex]scale\text{ factor =}\frac{final\text{ length }}{original\text{ length}}[/tex]so, let's take the longest side on each triangle
[tex]\begin{gathered} final\text{ length=12} \\ original\text{ length=8} \end{gathered}[/tex]replace and calculate
[tex]\begin{gathered} scale\text{ factor =}\frac{final\text{ length }}{original\text{ length}} \\ scale\text{ factor =}\frac{12}{8}=\frac{3}{2} \end{gathered}[/tex]therefore, the answer is
a) Yes, The scale factor is 3/2
I hope this helps you
Question 3 of 5 Shayla spent $260 on 4 chairs. To find out how much she spent on each chair, she did the following work in long division. 15 4) 260 60 0 Did she do the problem correctly? Why or why not?
we know that
To find out how much she spent on each chair
Divide the total cost by the number of chairs
so
[tex]\frac{260}{4}=65[/tex]therefore
She spent on each chair $65
Find the length of the third side. If necessary, write in simplest radical form.DV895
In order to solve the missing side for a right triangle, we can use the Pythagorean theorem
[tex]a^2+b^2=c^2[/tex]then, we rewrite the expression for on of the sides different from the hypotenuse
[tex]\begin{gathered} a^2=c^2-b^2 \\ a=\sqrt[]{c^2-b^2} \end{gathered}[/tex]replace with the values
[tex]\begin{gathered} a=\sqrt[]{(\sqrt[]{89})^2-5^2} \\ a=\sqrt[]{89-25} \\ a=\sqrt[]{64} \\ a=8 \end{gathered}[/tex]Hi I need help solving for each of the sides in this equation.CDABSolve to the nearest hundredth
Length of CD
From the picture, we know two sides and an angle of the triangle CDE. We define the sides and angle:
• a = EC = 440.68,
,• b = ED = 470.43,
,• c = CD = ?,
,• γ = 60° 06' 09''.
From trigonometry, we know that the Law of Cosines states that:
[tex]\begin{gathered} c^2=a^2+b^2-2ab\cdot\cos\gamma, \\ c=\sqrt{a^2+b^2-2ab\cdot\cos\gamma}. \end{gathered}[/tex]Where the angle γ and the sides a, b and c are defined by:
Replacing the values from above in the equation for side c, we get:
[tex]c=\sqrt{(440.68)^2+(470.43)^2-2\cdot440.68\cdot470.43\cdot\cos(60\degree06^{\prime}09^{\prime}^{\prime})}\cong457.10.[/tex]Length of AB
To compute the length of AB, first, we must compute the length of sides AE and EB.
Side EB
From the picture, we see a triangle ECA. Using the data of the picture, we have:
• EC = 440.68,
,• ∠E = 60° 06' 09'',
,• EA = ?,
,• ∠A = ?.
,• ∠C = 97° 17' 42''.
Angles ∠A, ∠E and ∠C are the inner angles of triangle ECA, so they must sum up 180°, so we have:
[tex]\begin{gathered} ∠A+∠E+∠C=180\degree, \\ ∠A=180\degree-∠E-∠C, \\ ∠A=180\degree-60\degree06^{\prime}09^{\prime\prime}-97\degree17^{\prime}42^{\prime\prime}=22°36^{\prime}9^{\prime\prime}. \end{gathered}[/tex]Now, we define the following sides and angles:
• c' = EC = 440.68,
,• γ' = ∠A = 22° 36' 9''
,• a' = EA = ?,
,• α = ∠C = 97° 17' 42''.
Now, from trigonometry, we know that the Law of Sine states that:
Using the equation that relates a' and c', we have:
[tex]\begin{gathered} \frac{a^{\prime}}{\sin\alpha^{\prime}}=\frac{c^{\prime}}{\sin\gamma^{\prime}}, \\ a^{\prime}=c^{\prime}*\frac{\sin\alpha^{\prime}}{\sin\gamma^{\prime}}. \end{gathered}[/tex]Replacing the values from above, we get:
[tex]EA=a^{\prime}=440.68*\frac{\sin(97°17^{\prime}42^{\prime\prime}^)}{\sin(22°36^{\prime}9^{\prime\prime})}[/tex]Side AE
From the picture, we see a triangle EDB. Using the data of the picture, we have:
• b' = ED = 470.43,
,• ∠E = 60° 06' 09'',
,• a' = EB = ?,
,• α' = ∠D = 180° - 87° 20' 24'' = 92° 39' 36'',
,• β' = ∠B = 180° - ∠D - ∠E = 180° - 92° 39' 36'' - 60° 06' 09'' = 27° 14' 15''.
Applying the law of sines, we have that:
[tex]\begin{gathered} \frac{a^{\prime}}{\sin(\alpha^{\prime})}=\frac{b^{\prime}}{\sin(\beta^{\prime})}, \\ EB=a^{\prime}=b^{\prime}*\frac{\sin(\alpha^{\prime})}{\sin(\beta^{\prime})}. \end{gathered}[/tex]Replacing the values from above, we get:
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Answer
s
[tex]8 \sqrt[5]{11} - 4 \sqrt[5]{11} [/tex]Simplify the expression
what is x? how would i find the value of
Given the Right Triangle ABC, you know that:
[tex]\begin{gathered} AB=29 \\ BC=9 \end{gathered}[/tex]In order to find the measure of the angle "x", you need to use the following Inverse Trigonometry Function:
[tex]\theta=sin^{-1}(\frac{opposite}{hypotenuse})[/tex]In this case, you can identify that:
[tex]\begin{gathered} \theta=x \\ opposite=BC=9 \\ hypotenuse=AB=29 \end{gathered}[/tex]Therefore, when you substitute values and evaluate, you get:
[tex]x=sin^{-1}(\frac{9}{29})[/tex][tex]x\approx18\text{\degree}[/tex]Hence, the answer is:
[tex]x\approx18\text{\degree}[/tex]Fred's car van travel 368 miles on one tank of gas. His has tank holds 16 gallons what is the unit rate for mules per gallon
16 gallons is needed for 368miles
Therefore
1 gallon is needed for 368/16 = 23miles
Hence the rate for miles per gallon is
Jeff decides to lease a $35,000 vehicle for 4 years. It is estimated that the car will be resold in two years at a price of$17,955. If the annual interest is 3%, what is the financing fee?$44.89O $87.50$66.19$151.30
Which is not a correct description of the graph below? nh -2TT -TK 2TT The graph of y = cos & shifted to the left by 34 units. Зл 2 The graph of y = sin e shifted to the left by n units. O y = sin(0 + 21) = O y = cos(0+ y = 3 Зл 2
Verify each statement
N 1 -----> is true
because
y=cosx , shifted to the left by 3pi/2 is y=cos(x+3pi/2)
N 2 ----> is false
N 3 -----> is true
N4 ----> is true
therefore
the answer is option N 2Answer question number 18. The question is in the image.
18.
Given:
[tex]g(x)=3sin2x[/tex]Required:
We need to graph the function and find the transformation from the parent function.
Explanation:
The given equation is of the form.
[tex]g(x)=Asin(Bx+C)[/tex]where A =3, B=2, and C=0.
We know that A is amplitude.
[tex]Amplitude=3[/tex][tex]Period=\frac{2\pi}{|B|}[/tex]Substitute B=2 in the equation,
[tex]Period=\frac{2\pi}{|2|}[/tex][tex]Period=\pi[/tex]Recall that the amplitude of a function is the amount by which the graph of the function travels above and below its midline.
The distance between the maximum point and midline is 3.
The time interval between two waves is known as a Period
The time interval between two waves is pi.
The graph of the function.
[tex]The\text{ parent function is f\lparen x\rparen=sinx.}[/tex]Recall that the amplitude stretches or compresses the graph vertically.
Here we have amplitude =3. it is a positive value.
The parent function stretches vertically by 3 units.
Recall that the period stretches or compresses the graph horizontally.
Here we have the period is pi.
The parent function compresses horizontally by pi.
Final answer:
[tex]Amplitude=3[/tex][tex]Period=\pi[/tex]The transformation is stretched vertically by 3 units and compressed horizontally by pi.