Variables:
x: hawk fans
y: cyclone fans
The basketball game had 600 people in attendance means:
x + y = 600
The ratio of hawk fans to cyclone fans is 2:10 means
[tex]\begin{gathered} \frac{x}{y}=\frac{2}{10} \\ 10x=2y \\ \frac{10x}{2}=y \\ 5x=y \end{gathered}[/tex]Substituting the last equation into the first equation, we get:
x + 5x = 600
6x = 600
x = 600/6
x = 100
And the value of y is:
y = 5*100
y = 500
There were 500 - 100 = 400 more cyclone fans
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write the slope intercept form of an equation though given points
through (3,-5) and (1,3)
slove the equation 4c + 7 = 23
We need to solve the expression:
[tex]4c+7=23[/tex]The first step is to subtract "7" on both sides.
[tex]\begin{gathered} 4c+7-7=23-7 \\ 4c=16 \end{gathered}[/tex]Then we need to divide both sides by 4.
[tex]\begin{gathered} \frac{4c}{4}=\frac{16}{4} \\ c=4 \end{gathered}[/tex]The result of the equation is "c=4".
Only quadratic functions can be transformed. true or false
It is false, that only quadratic functions can be transformed.
Given that,
To justify the statement, "Only quadratic functions can be transformed."
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
It is not necessary that only quadratic functions can be transformed, all the functions can be transformed regardless of their nature such as linear functions, polynomial functions etc.
Thus, It is false, that only quadratic functions can be transformed.
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Shannon invests money in a bank account which gathers
compound interest each year.
After 5 years there is $673.40 in the account.
After 8 years there is $737.99 in the account.
Work out the annual interest rate of the bank account.
Give your answer as a percentage to 1 d.p.
By using the concept of compound interest, rate of interest is 3.1 %
What is compound interest?
If the interest on a certain principal at a certain rate over a certain time increase exponentially rather than linearly, the interest earned is called Compound interest.
If the principal is P, rate is r and time is t, then amount is
[tex]A = P(1 + \frac{r}{100})^n[/tex]
Let the principal be $P and the rate be r% per annum
After 5 years there is $673.40 in the account.
[tex]673.40 = P(1 + \frac{r}{100})^5\\[/tex]............. (1)
After 8 years there is $737.99 in the account.
[tex]737.99 = P(1 + \frac{r}{100})^8[/tex] ................. (2)
Dividing (2) by (1),
[tex](1 +\frac{r}{100})^3 = 1.096\\\\1 + \frac{r}{100} = (1.096)^{\frac{1}{3}}\\\\1 + \frac{r}{100} = 1.031\\\\\frac{r}{100} = 1.031 -1\\\\\frac{r}{100} =0.031\\\\r = 0.031 \times 100\\[/tex]
r = 3.1 %
Rate is 3.1 %
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For a certain casino slot machine, the odds in favor of a win are given as 67 to 33. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive. The probability is ___
Data:
• Odds in favor of a win are given as 67 to 33.
Procedure
• We have to find the total sample (,T,), which can be calculated as follows:
[tex]T=67+33=100[/tex]Then, to calculate the probability, we have to divide the odds in favor of a win by T.
[tex]\frac{67}{100}=0.67[/tex]Answer: 0.67
There is a 40% chance that it is rainy in California. If there are 365 days in a year, how many of them would you expect to be rainy?
It is expected that 146 days will be rainy
Based on the given percentage, we want to calculate the number of rainy days
What we have to do here is to multiply the percentage by the number of days
That would be 40% of 365 days
We have this as;
[tex]\frac{40}{100}\times365\text{ = 146}[/tex]Connor was given a box of assorted chocolates for his birthday. Each night, Connortreated himself to some chocolates. There were originally 18 chocolates in the boxand after 3 nights, there were 9 chocolates remaining in the box. Write an equationfor C, in terms of t, representing the number of chocolates remaining in the box tdays after Connor's birthday.
The equation for C in terms of t is C = 18 – 3t.
Algebra is the area of mathematics that aids in expressing issues or circumstances into mathematical expressions.
Given that Connor was given a box of assorted chocolates for his birthday
The box originally contained 18 chocolates.
There were still 9 chocolates in the box after three nights.
Now we have to find the equation for C in terms of t
18 – 9 = 9
After 3 nights
9 / 3 = 3
18 = chocolates at the beginning.
C = 18 – 3t
Therefore the equation for C in terms of t is C = 18 – 3t.
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help meeeeeeeeeeeeeeeeeeee pleaseee rnnnn rn!!!!
The length of shorter feet is 2.5 ft and the length of longer feet is 6.5 ft.
By Pythagorean theorem,
[tex]( Hypotenuse)^{2} = (Base)^{2}+ (Perpendicular)^{2}[/tex]
Let base = x
perpendicular = x+4
Hypotenuse = 7
Putting the value in equation,
[tex]7^{2} = x^{2} +(x+4)^{2}[/tex]
[tex]49 = x^{2} +x^{2}+8x+16[/tex]
[tex]2x^{2} +8x+16-49=0[/tex]
[tex]2x^{2} +8x-33=0[/tex]
[tex]x = \frac{-8 + \sqrt{64 - 4(2)(-33)} }{2*2}[/tex] or [tex]\frac{-8 - \sqrt{64 - 4(2)(-33)} }{2*2}[/tex]
[tex]x=\frac{-8 + \sqrt{64 +264} }{4}[/tex] or [tex]\frac{-8 - \sqrt{64 +264} }{4}[/tex]
[tex]x = \frac{-8 + \sqrt{384} }{4}[/tex] or [tex]\frac{-8 - \sqrt{384} }{4}[/tex]
[tex]x = \frac{-8+18.1}{4}[/tex] or [tex]\frac{-8-18.1}{4}[/tex]
[tex]x = \frac{10.1}{4}[/tex] or [tex]\frac{-26.1}{4}[/tex]
[tex]x = 2.5[/tex] or [tex]-6.5[/tex]
As, length can't be negative, we will take x = 2.5
Therefore, x+ 4 = 2.5 + 4
= 6.5
Hence, the length of shorter feet is 2.5 ft and the length of longer feet is 6.5 ft.
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can you help me find BD. under the letter A the number is 25°
arc BD is 25°
Explanation:We would apply the secant-secant theorem:
[tex]\begin{gathered} \angle A\text{ =}\frac{large\text{ arc - small arc}}{2} \\ \angle A\text{ =}\frac{arc\text{ CE - arc BD}}{2} \end{gathered}[/tex]angle A = ∠A =25°
arc BD =?
arc CE = 100°
[tex]\begin{gathered} 25\text{ = }\frac{100-arc\text{ BD}}{2} \\ \text{cross multiply:} \\ 2(25)\text{ = 100 - arc BD} \end{gathered}[/tex][tex]\begin{gathered} 50\text{ = 100 - arc BD} \\ \text{subtract 100 from both sides:} \\ 50\text{ - 100 = 100 - 100 - arc BD} \\ -50\text{ = - arc BD} \end{gathered}[/tex][tex]\begin{gathered} \text{DIvide both sides by -1:} \\ \frac{-50}{-1\text{ }}=\frac{-arc\text{ BD}}{-1} \\ \text{arc BD = 50}\degree \end{gathered}[/tex]2/9x20 as a fraction
Answer:
40/9 OR 4 4/9
Step-by-step explanation:
2/9 x 20 = 2*20/9 = 40/9
What happens if the rate of change is not constant in a function?
Answer:
time will be a straight line, and you can find the rate of change by calculating the slope of the line. If the rate of change is not constant, a graph of the measured quantity vs. time will be curved instead of straight
Step-by-step explanation:
Answer:
When the rate of change is constant, the graph results in a straight line. When the rate of change is not constant, the graph will include a curved line.
Step-by-step explanation:
please answer this question
The value of m<2 = 107
Given:
m<SOX = 160
m<1 = x+14
m<2 = 3x - 10
x + 14 + 3x - 10 = 160
4x + 14 - 10 = 160
4x + 4 = 160
4x = 160 - 4
4x = 156
divide by 4 on both sides
4x/4 = 156/4
x = 39
m<2 = 3*39 - 10
= 117 - 10
= 107
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6
Simplify the expression: (1318) + 24 ÷ 6
How many people did Trevor survey?
74
92
107
137
Answer:
92 I think because in my class I heard my friend tell me
In ΔOPQ, o = 9.2 cm, p = 2.4 cm and ∠Q=37°. Find the length of q, to the nearest 10th of a centimeter.
The length of q, to the nearest 10th of a centimeter is 7.6 cm.
Given in question,
In ΔOPQ,
o = 9.2 cm
p = 2.4 cm
∠Q = 37°
Cosine formula ⇒ cos θ = [tex]\frac{o^{2}+p^{2}-q^{2} }{2op}[/tex]
Putting the values in equation,
cos 37 = [tex]\frac{(9.2)^{2}+(2.4)^{2}-q^{2} }{2*9.2*2.4}[/tex]
0.799 = [tex]\frac{84.64 + 5.76-q^{2} }{44.16}[/tex]
0.799*44.16 = 90.4 - [tex]q^{2}[/tex]
32.28 = 90.4 - [tex]q^{2}[/tex]
[tex]q^{2}[/tex] = 90.4 - 32.28
[tex]q^{2}[/tex] = 58.12
[tex]q = \sqrt{58.12}[/tex]
[tex]q = 7.63[/tex]
q = 7.6 cm (to nearest 10th)
Hence, length of q is 7.6 cm.
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Study the figures, figure 1 is similar to figure 2Part A : Describe a series of transformations and dilations that map figure 1 to figure 2Part 2: Describe a second series of transformations and dilations that map figure 1 to figure 2
In order to go from figure 1 to figure 2, there are a number of different transformations that can be selected.
First, notice that figure 2 is exactly three times as large as figure 1, therefore, there has been a dilation by a factor of three (3) that took place .
So Let's say that we do the dilation first.
Step 1: Dilation by a factor of "3" using the point (-1, -2) which is one of the vertices of the triangle, for reference. Then, the new triangle would have new coordinaes for the vertices at the points:
(-1, -2) (-1, 1) and (-6, -2)
I am making a drawing to show the change (give me a little time)
So, we see that the dilated triangle is represented by the green one in the image above.
Step 2: we are now going the "reflect the green triangle around the horizontal line y = 2 represented by the blue line . When we reflect the green triangle around that line, we obtain the orange triangle.
Step 3: we are going to do another reflection, this time a reflection around the vertical line x = 1 (noted in purple in the image above). After this, we obtain the triangle in figure 2.
So we
Multiply the two polynomials (3a² + 5a - 2)(5a² - 3a + 4)
SOLUTION
The polynomials expression given are
[tex]\mleft(3a^2+5a-2\mright)\mleft(5a^2-3a+4\mright)[/tex]Expand the expression by distributing the parentheses
[tex]3a^2\cdot\: 5a^2+3a^2\mleft(-3a\mright)+3a^2\cdot\: 4+5a\cdot\: 5a^2+5a\mleft(-3a\mright)+5a\cdot\: 4-2\cdot\: 5a^2-2\mleft(-3a\mright)-2\cdot\: 4[/tex]Simplify
[tex]\begin{gathered} 15a^4-9a^3+12a^2+25a^3-15a^2+20a-10a^2+6a-8 \\ \text{Rearranging and simplify} \\ 15a^4-9a^3+25a^3+12a^2-15a^2-10a^2+20a+6a-8 \\ 15a^4+16a^3-13a^2+26a-8 \end{gathered}[/tex]Hence, the answer is
[tex]15a^4+16a^3-13a^2+26a-8[/tex]yo i need some help this determines weather i pass or fail
To make 4 dozen cookies she would need
→ 3/2 cup peanut butter
→ 3 cup of vegetable shortening
→ 1 1/2 cups of firmly packed light brown sugar
→ 6 tablespoons of milk
→ 2 3/2 tablespoons of vanilla extract
→ 2 cups of flour
→ 3/2 teaspoon of baking soda
→ 1/2 teaspoon salt
To make 4 dozen cookies
she will need double the items which are mentioned in the list
thus the required list will look like this
3/4 × 2 = 3/2 cup peanut butter
3/2 cup of vegetable shortening = 3/2 × 2 = 3 cup of vegetable shortening
1 1/4 cups of firmly packed light brown sugar = 1 1/4 × 2 = 1 1/2 cups of firmly packed light brown sugar
3 tablespoons of milk = 3 × 2 = 6 tablespoons of milk
2 3/4 tablespoons of vanilla extract = 2 3/2 tablespoons of vanilla extract
1 large egg = 1× 2 = 2 large eggs
1 1/2 cups flour = 1 1/2×2 = 1 + 1 = 2 cups of flour
3/4 teaspoon baking soda = 3/2 teaspoon of baking soda
1/4 teaspoon salt = 1/4 × 2 = 1/2 teaspoon salt
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There are two integers that
multiply to -45 and combine to -4. Find
the two integers, then the LARGER
integer is your answer for this question.
Answer:
5
Step-by-step explanation:
-9 × 5 = -45
-9 + 5 = -4
5 is greater than -9, therefore 5 is the answer
5. 2. A rectangular print is 36 inches long and 24 inches wide. It will be placed inside a rectangular frame that is 2 inches wide on all sides. What is the area when the print is inside the frame A. 864 in. B. 960 in? C. 980 in. D. 1,120 in.
Since the frame has 2 inches wide on all sides, the frame measures:
Then, the area of the frame is
[tex]\begin{gathered} A=\text{basexheight} \\ A=40\times28 \end{gathered}[/tex]which gives
[tex]A=1120in^2[/tex]then, the answer is 1120 inches squared, which corresponds to option D.
Find the slope (-19,12) (-9,1)
Answer:
m= -11/10
Step-by-step explanation:
Refer to formula m= y2-y1
x2-x1
1-12 = -11 (negative bc 1 comes first but is less than 12.)
Think of it as -12+1 it would be -11 going towards 0.
-9--19 = 10
There are 1.5 litres of water in a bottle.
There are 250 millilitres of water in another bottle.
Work out the total amount of water in the two bottles
Answer:
1.75 liters
Step-by-step explanation:
250 mililters is a quarter of 1 litre
Clare has $102.38 in her savings account. At the ATM, she deposits 3 checks she received for her birthday. Each check was written for $15.00. Then, she withdraws $20 in cash. What is Clare's new account balance?
Answer:
127.38
Step-by-step explanation:
Answer:
127.38
Step-by-step explanation:
15 x 3 = 45
(102.38 + 45) - 20 = 127.38
When using an equivalent fraction to find a percent why do you write 100 as the denominator?
We do so beacuse it is easy to convert a fraction to a percent when the denominator is 100.
What is equivalent fraction?Equivalent fractions are the fractions that have different numerators and denominators but are equal to the same value.
What is denominator?Denominator is the part of a fraction that is below the line and that functions as the divisor of the numerator.
What is percentage?A percentage or percent is a fraction that always has the denominator as 100.
When using an equivalent fraction to find a percent we write 100 as denominator.
If a fraction does not have a denominator of 100, you can convert it to an equivalent fraction with a denominator of 100, and then write the equivalent fraction as a percent.
We do so because it is easy to convert a fraction to a percent when the denominator is 100.
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Light intensity (I) is proportional (a) to the inverse square of distance (d) of a subject from a lightsource. The relationship in intensities for subjects at different distances from the same source canbe likewise seen as a ratio or proportional relationship.I x 1 1A proportional relationship can be mathematically expressed as follows for light intensity (I) inlumens when a subject is at the light source.=Lumens at origin or sourceSo, if a light intensity (I) is 569 lumens at the source, what is the light intensity (I) at 9 distancefrom the source,?Round the value to the nearest tenth if necessary. You do not need to include a label for lumens.Only the number, rounded to the tenth, will be necessary.
ANSWER
The light intensity is 7.0
STEP-BY-STEP EXPLANATION:
What to find? The value of the proportionality constant.
Given parameters
• Light intensity = 569 lumens
,• Distance = 9
According to the question, Light intensity (I) is proportional to the inverse square of the distance.
This can be expressed mathematically as
Let the intensity of light be represented as I
Let the distance be represented as d
[tex]I\text{ }\propto\text{ }\frac{1}{d^2}[/tex]The next thing is to introduce a constant k
[tex]\begin{gathered} I\text{ = }\frac{K\cdot\text{ 1}}{d^2} \\ I\text{ = }\frac{K}{d^2} \end{gathered}[/tex]Recall that,
I = 569 lumens
d = 9
The next thing is to substitute the parameters into the above formula
[tex]\begin{gathered} \frac{Lumens\text{ at current distance}}{\text{Lumens at origin or source}}\text{ = }\frac{1}{d^2} \\ \frac{\text{Lumens at current distance}}{\text{5}69}\text{ = }\frac{1}{(9)^2} \\ \frac{\text{Lumens at current distance}}{\text{5}69}\text{ = }\frac{1}{81} \\ \text{Cross multiply} \\ 569\cdot\text{ }1\text{ = Lumens at current distance }\cdot\text{ 81} \\ \text{Divide both sides by 81} \\ \frac{569}{81}\text{ = }\frac{Lumens\text{ at current distance }\cdot\text{ 81}}{81} \\ \text{Lumens at current distance = 7.0} \end{gathered}[/tex]is 6(2x-7)-3=12x-21 a no solution one solution or infinitely
Step-by-step explanation:
let's do the operations :
6(2x - 7) - 3 = 12x - 21
12x - 42 - 3 = 12x - 21
-45 = -21
that is never true, no matter what values for x we come up with.
and therefore, there is no solution.
If you travel a 150 miles in 3 hours what was your average rate of speed
Distance (D): 150 miles
Time (t): 3 hours
[tex]Speed=\frac{D}{t}=\frac{150}{3}=50[/tex]Answer: 50 miles / hour
Suppose you are the manager of a firm. The accounting department has provided cost estimates, and the sales department sales estimates, on a new product. Analyze the data they give you, determine what it will take to break even, and decide whether to go ahead with production of the new product The product has a production cost function C(x)=560x + 17,080 and a revenue function R(x) = 700xThe break-even quantity is ______units.
Consider that the break-even quantity is the one corresponding to which the profit is zero i.e. the production cost becomes equal to the revenue earned.
Equate the functions and solve for the break-even quantity as follows,
[tex]\begin{gathered} C(x)=R(x) \\ 560x+17,080=700x \\ 700x-560x=17,080 \\ 140x=17,080 \\ x=122 \end{gathered}[/tex]Thus, the break-even quantity is 122 units.
Compare: 4.3 x 10^6 O 12 x 10^5A.>B.
To check the bigger or smaller number, we can adjust the numbers such that they both have the same exponential power.
The first number can be written as shown below:
[tex]4.3\times10^6=4.3\times10\times10^5=43\times10^5[/tex]Now, both numbers have the same exponent. Therefore, we can compare the numbers 43 and 12.1.
Observation of the numbers on the number line shows that:
[tex]43>12.1[/tex]Therefore, we have that:
[tex]43\times10^5>12.1\times10^5[/tex]The correct option is OPTION A.
Given f(x)=3x^3 - 4x^2 + 2x - 1 and g(x) = x - 4, state the quotient and remainder of f(x)/g(x), in the form q(x) + r(x)/g(x)
Dividing f(x) = 3x³ - 4x² + 2x - 1 by g(x) = x - 4 will yield a quotient of q(x) = 3x² - 8x + 34 and a remainder of 135, that is (3x² - 8x + 34) + 135/(x - 4).
Calculating for the quotient and remainderApplying the long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder.
We shall divide the dividend f(x) = 3x³ - 4x² + 2x - 1 by the divisor g(x) = x - 4 as follows;
3x³ divided by x equals 3x²
x - 4 multiplied by 3x² equals 3x³ - 12x²
subtract 3x³ - 12x² from 3x³ - 4x² + 2x - 1 will result to 8x² + 2x - 1.
8x² divided by x equals 8x
x - 4 multiplied by 8x² equals 8x² - 32x
subtract 8x² - 32x from 8x² + 2x - 1 will result to 34x - 1.
34x divided by x equals 34
x - 4 multiplied by 34 equals 34x - 136
subtract 34x - 136 from 34x - 1. will result to a remainder of 135.
Therefore by the long division method, f(x) = 3x³ - 4x² + 2x - 1 divided by g(x) = x - 4 gives a quotient q(x) = 3x² - 8x + 34 with a remainder of 135.
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