We will have that the contrapositive statement is:
*If you do not wear a helmet, then you do not play a sport.
An experiment consists of spinning the spinner shown. All outcomes are equally likely. Find P(<7). Express your answer as a fraction in simplest forn
There are 8 total outcomes. Now, we need to find where P(<7).
This means the outcomes where the number is less than 7.
There are 6 numbers under the 7 = 1,2,3,4,5,6
The probability is given by the next formula:
[tex]P=\frac{\text{Number of favorable outcomes}}{\text{Total of possible outcomes}}[/tex]Where:
Number of favorable outcomes = 6
Total of possible outcomes = 8
Replacing these values:
[tex]P=\frac{6}{8}[/tex]Simplify the expression, divide both numbers by 2:
[tex]P=\frac{3}{4}[/tex]The correct answer is the second one.
What is eight times the square root of two square root of two
Given expression is
[tex]8\sqrt[]{2\sqrt[]{2}}[/tex]Now, solving it as:
[tex]8\sqrt[]{2\sqrt[]{2}}=8\cdot2^{\frac{3}{4}}[/tex]So,
[tex]8\cdot2^{\frac{3}{4}}[/tex]is the required solution.
.The balance on Mr. Finch's credit card is -$210. It is 3 times the balance on Mr. Nguyen's credit card. Find the quotient -210 ÷ 3 and explain what it means in this context.
Given: Balance of Finch's card is = -$210.
This is 3 times the balance on Mr. Nguyen's credit card.
To find: -210/3.
Explanation:
Let the balance on Mr. Nguyn's card be = x.
The balance of Mr. Finch's card is 3 times Mr. Nguyen's card.
Mathematically this can be expressed as:
[tex]-210=3x[/tex]Now, the value of x or "Mr. Nguyen's credit card balance" can be calculated as:
[tex]\begin{gathered} x=\frac{-210}{3} \\ x=-70 \end{gathered}[/tex]Therefore, the term -210/3 represents Mr. Nguyen's credit card balance and its value is -$70.
Final Answer: The term -210/3 represents Mr. Nguyen's credit card balance and its value is -$70.
At the end of the first half of a basketball game, UCONN and SCSU were tied. During the second half UCONN scored 48 points and SCSU scored twice as many points as they had in the first half. What was the final score of UCONN won by 2 points?
Okay, here we have this:
Let's take the endpoints of UCONN as x and those of SCSU as y. So:
x=y+2
And:
So the UCONN points of the first half are: x/3. And since they were tied SCSU had the same points at the first half.
And those UCONN points of the second half are 2x/3, and the SCSU points at the end were then x/3+48.
So, we obtain that:
y=x/3+48
x=(x/3+48)+2
x=x/3+50
x-x/3=50
2x/3=50
2x=150
x=75
And, replacing in y:
y=75/3+48=25+48=73
Finally we obtain that the final score was: UCONN 75: SCSU 73
What is the slope of y= -4
Hello!
We have the equation of the line y = -4.
Let's put this equation in a cartesian plane:
Notice that this equation will be always constant. So, as we just have a straight line with no inclination, the slope is 0.
Which expression has a quotient of about 7? F 7:2 G 23 : 7 H 36 : 5 J 13:6 Type here to search O | a 3
The question simply means when you divide two numbers, the one that will result to 7
Hence;
36 ÷ 5 = 7.2
H is the correct option
For which equation would x = 12 NOT be a solution?Options:X\1=12x\4=2x\3=4x\2=6
Given:
[tex]x=12[/tex]is given.
Required:
Which option is not appropriate.
Explanation:
Now we check all the option for this
[tex]\begin{gathered} \frac{x}{1}=12 \\ x=12 \end{gathered}[/tex]which is appropriate
[tex]\begin{gathered} \frac{x}{4}=2 \\ x=8 \end{gathered}[/tex]which is not appropriate
[tex]\begin{gathered} \frac{x}{3}=4 \\ x=12 \end{gathered}[/tex]which is appropriate
[tex]\begin{gathered} \frac{x}{2}=6 \\ x=12 \end{gathered}[/tex]which is appropriate
Final answer:
Sandra has a bag of animal cookies. The bag contains the cookies below. What is the probability that Sandra chooses a bear cookie first, eats it, and thenselects a lion cookie?9 lions5 elephants 3 tigers9 Bears 18/5218/5181/65081/676
ANSWER:
The probability of choosing a bear first then a lion is 81/650
SOLUTION:
This is a permutation and probability problem
The total cookies are 26
The combination for the total cookies is 26 * (26-1) = 26*25
The permutation for choosing a bear then a lion is 9 * 9
The probability is the permutation of choosing the bear over the permutation in total combination for total cookies
[tex]\frac{9\times9}{26\times25}=\frac{81}{650}[/tex]Write (3-2i)^3 in simplest a + bi form.
SOLUTION
We want to write
[tex]\begin{gathered} \mleft(3-2i\mright)^3\text{ in simplest form } \\ a+bi \end{gathered}[/tex]This means we have to expand
[tex](3-2i)^3[/tex]Applying perfect cube formula, we have
[tex]\begin{gathered} \mleft(a-b\mright)^3=a^3-3a^2b+3ab^2-b^3 \\ \text{where } \\ a=3,\: \: b=2i \end{gathered}[/tex]We have
[tex]\begin{gathered} (a-b)^3=a^3-3a^2b+3ab^2-b^3 \\ \mleft(3-2i\mright)^3=3^3-(3\times3^2\times2i)+(3\times3\times(2i)^2)-(2i)^3_{} \\ =27-(27\times2i)+(9\times(2i)^2)-(2i)^3_{} \end{gathered}[/tex]This becomes
[tex]\begin{gathered} \text{note that i = }\sqrt[]{-1} \\ i^2=\sqrt[]{-1^2}=-1 \\ So\text{ we have } \\ =27-(27\times2i)+(9\times(2i)^2)-(2i)^3_{} \\ 27-54i+(9\times4i^2)-(8i^2\times i) \\ 27-54i+(9\times4\times-1)-(8\times-1\times i) \\ 27-54i-36+8i \\ -9-46i \end{gathered}[/tex]Hence the answer is
[tex]-9-46i[/tex]A Snap Cube PrismA rectangular prism is 3 units high, 2 units wide, and 5 units long. What is its surfacearea in square units? Explain or show your reasoning (work).
62 u² (square units)
1) A rectangular prism is made up of 6 rectangles. So we can write them out:
2 rectangles (3 x 2)
2 rectangles ( 5 x 2)
2 rectangles ( 5 x 3)
2) Therefore the Total Surface Area of that prism can be found by applying the formula for the area of each rectangle times 2. Like this:
[tex]\begin{gathered} \text{TSA}=\text{ 2(3}\times2\text{ +5}\times2+5\times3) \\ \text{TSA}=\text{ 2(6 +10+15)} \\ \text{TSA}=\text{ 2(31)} \\ \text{TSA}=62 \end{gathered}[/tex]3) Hence the answer is 62 u² (square units)
Can I please get some help with this equation? Evaluate and simplify log of csc(5pi/6) multiplied by csc(pi/4). Explain your work.
1) Considering that the 1st property of Logarithms tells us:
[tex]\log _ab\text{ =c}\Leftrightarrow a^c=b[/tex]2) Let's evaluate that:
[tex]\begin{gathered} \log _{\csc (\frac{5\pi}{6})}(\frac{\csc \pi}{4})=x\Rightarrow\csc (\frac{5\pi}{6})^x=\csc (\frac{\pi}{4}) \\ \\ \csc (\frac{5\pi}{6})^x=\csc (\frac{\pi}{4}) \\ \log \csc (\frac{5\pi}{6})^x=\log \csc (\frac{\pi}{4}) \\ \text{x}\log \csc (\frac{5\pi}{6})^{}=\log (\sqrt[]{2}) \\ x\log (2)=\text{ log(}\sqrt[]{2}) \\ x=\frac{\log\sqrt[]{2}}{\log\text{ 2}} \\ x=\frac{1}{2} \end{gathered}[/tex]• Notice that we've descended that exponent x, to become a factor (3rd line).
,• Then divided both log with a common base, in this case, base 10.
3) Hence that equation yields 1/2 as its result.
The illumination provided by a car's headlight varies inversely as the square of the distance from the headlight. A car's headlight produces an illumination of 3.75 footcandles at a distance of 40 feet. What is the illumination when the distance is 50 feet?
The illumination should be represented by y, while the distance from the headlight should be represented by x, therefore the inverse relationship between both variables is shown as;
[tex]\begin{gathered} y=\frac{k}{x^2} \\ \text{When y=3.75, then x=40. Therefore;} \\ 3.75=\frac{k}{40^2} \\ 3.75=\frac{k}{1600} \\ 3.75\times1600=k \\ k=6000 \\ \text{Hence, when the distance (x) is 50 feet} \\ y=\frac{k}{x^2} \\ y=\frac{6000}{50^2} \\ y=\frac{6000}{2500} \\ y=2.4 \end{gathered}[/tex]The illumination at a distance of 50 feet is therefore 2.4 footcandles
Tyler has already taken 35 credit hours and plans on taking 15 hours per semester until he graduates. Does this describe a linear or exponential function?
Given:
Tyler has already taken 35 credit hours.
He plans on taking 15 hours per semester.
Let the number of semesters = x
So, the function that describes this will be:
[tex]y=15x+35[/tex]So, the function represents a line.
So, the answer will be a Linear function.
put each improper fraction into a mixed number 50/9
Divide the numerator by the denominator:
50 divided by 9 = 5 with a reminder of 5
Write the whole number (5) , and use the remainder as a numerator and 9 as the numerator:
5 5/9
A=1/2(a+b)h solve for h can you please explain as well?
h = 2A/(a+b)
Explanation:
A=1/2(a+b)h
To solve for h, we will make h the subject of formula
The first thing we will do is bring the 1/2 to the other side of the equation:
[tex]\begin{gathered} A\text{ = }\frac{(a+b)h}{2}\text{ cross multiply} \\ 2A\text{ = (a+b)h} \end{gathered}[/tex]To make h stand alone, we would divide both sides by the values in the bracket:
[tex]\begin{gathered} \frac{2A}{(a+b)}\text{ = }\frac{(a+b)h}{(a+b)} \\ h\text{ = }\frac{2A}{a\text{ + b}} \end{gathered}[/tex]Therefore, h = 2A/(a+b)
how to solve 2(q+4)=16how to solve 7j+2=12+5jhow to solve 12z=60-3z
Answer:
Given that to solve
a) 2(q+4)=16
we get,
[tex]\begin{gathered} 2\mleft(q+4\mright)=16 \\ 2q+8=16 \end{gathered}[/tex][tex]2q=16-8[/tex][tex]2q=8[/tex]Dividing 2 on both sides we get,
[tex]q=4[/tex]Answer is: q=4
b)7j+2=12+5j
we get,
[tex]7j+2=12+5j[/tex][tex]7j-5j=12-2[/tex][tex]2j=10[/tex]Dividing 2 on both sides, we get
[tex]j=10[/tex]c) 12z=60-3z
we get,
[tex]12z=60-3z[/tex][tex]12z+3z=60[/tex][tex]15z=60[/tex]Dividing 15 on both sides we get,
[tex]z=4[/tex]
Solve in inequality 0.2 (30 + x). - 0.3 (30-x) >2
The inequality 0.2 (30 + x) - 0.3 (30 - x) >2 is solved to get x > 10
How to solve the inequalityThe given inequality is 0.2 (30 + x) - 0.3 (30 - x) >2
0.2 (30 + x) - 0.3 (30 - x) >2
expanding the parenthesis
6 + 0.2x - 9 + 0.3x > 2
collecting like terms
6 - 9 + 0.2x + 0.3x > 2
-3 + 0.5x > 2
0.5x > 2 + 3
0.5x > 5
dividing by the coefficient of x which is 0.5
x > 10
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Given that f(x) = 9x2 - 180 = 0, find x. A) x = +2 V5 B) x = +3 v5 C) x = +5 V2 D) x=+5 v3
Given data:
The given function is f(x)=9x^2-180=0
The given expression can be written as,
[tex]\begin{gathered} 9x^2-180=0 \\ 9(x^2-20)=0 \\ (x^2-20)=0 \\ x=\pm2\sqrt[]{5} \end{gathered}[/tex]Thus, option (A) is correct.
determine whether the graph of the given equations are parallel, perpendicular, or neither.y=2x+15y= -2x+3
1. When two lines have the same slope they are parallel.
2 . When the quotient of two lines is -1 they are perpendicular.
The slope of
y = 2x + 15 is 2
the slope of
y = -2x + 3 is -2
since -2/2 = -1 they are perpendicular :)
V = πr (R²-r²)
make r the subject of the formula
The subject of the formula is [tex]\pi r = {r(R^{2}- r^{2})}[/tex]
Given,
V = πr (R²-r²)
then to find r in terms of the other values divide both the sides by the multiplier of r.
r is multiplied by πr²
Now divide both sides by V
[tex]\frac{V}{\pi r } = \frac{\pi r(R^{2}- r^{2})}{\pi r}[/tex]
[tex]\frac{V}{\pi r } = {(R^{2}- r^{2})}[/tex]
[tex]{\pi r } = \frac{{(R^{2}- r^{2})}}{V} \\\\\pi r^{2} = {r(R^{2}- r^{2})}[/tex]
Hence the answer is the subject of the formula is [tex]\pi r = {r(R^{2}- r^{2})}[/tex]
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a researcher wants to determine the number of televisions in a household.he conducts a survey of 40 random select house and I obtains data in accompying tabe. what is the relative frequency distribution of the data
The relative frequency (RF) can be calculated as follows:
[tex]RF=\frac{F}{\sum ^{}_{}F}[/tex]where RF is the relative frequency, F is the value of the frequency, and ∑F represents the sum of all frequencies.
Using a spreadsheet, we can get the following table:
Based on this table, we can see that ∑F = 40. Thus, we have to divide each frequency by 40 to get the relative frequency. As an example, using the first, second, and third row:
[tex]RF_1=\frac{1}{40}=0.025[/tex][tex]RF_2=\frac{15}{40}=0.375[/tex][tex]RF_3=\frac{13}{40}=0.325[/tex]Answer:
Determine the point estimate of the population mean and margin of error for the confidence interval.
Lower bound is 17, upper bound is 29.
The point estimate of the population mean is
The margin of error for the confidence interval is
...
The point estimate of the population mean is 23 and the margin of error for the confidence interval is 6.
In the given question, we have to find the value of the point estimate of the population mean and the margin of error for the confidence interval.
From the given question,
Lower bound is 17.
Upper bound is 29.
So the point estimate of the population mean is
Point Estimate = (Lower Bond+Upper Bond)/2
Point Estimate = (17+29)/2
Point Estimate = 46/2
Point Estimate = 23
Now finding the margin of error for the confidence interval.
Margin of error = Upper Bound-Point Estimate
Margin of error = 29-23
Margin of error = 6
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17. What is the value of x in the rhombusbelow?AC(x+40)B3x"D
Remember that
In a rhombus, diagonals bisect each other at right angles (perpendicular)
so
that means
(x+40)+(3x) =90 degrees ---------> by complementary angles
solve for x
4x+40=90
4x=90-40
4x=50
x=12.54. Write an equation for a line that isperpendicular to y = -4.
The equation y = -4 is a horizontal line at the point -4 in the y-axis.
In order to find a perpendicular line to this equation, we can choose any vertical line in the form:
[tex]x=a[/tex]Where 'a' is any real constant.
So an equation for a line perpendicular to y = -4 would be:
[tex]x=2[/tex]an average bath use 35 liters if water,while a five minutes shower only uses 12.5 liters of water.how many milliliters are you saving if you take a five minutes shower instead of a bath
To find the saving of water you have to substract the average bath to the average shower
[tex]35-12.5=22.5[/tex]So you save 22.5 liters of water.
Now we have to convert the liters to mililiters, this can be done if we rememeber that a liter contains 1000 mililiters, then we multiply our result by 1000.
[tex]22.5(1000)=22500[/tex]Therefore we save 22500 mililiters of water.
If ABCDE is reflected over the x-axis and then translated 3units left, what are the new coordinates B?E..ADO A. (1, -2)O B. (7,-2)C. (4, -2)D. (-7,2)CBX
Recall that the rule of transformation for a point (x,y) reflected over the x-axis is:
[tex](x,y)\rightarrow(x,-y),[/tex]and the rule of transformation for a point translataled n units to the left is:
[tex](x,y)\rightarrow(x-n,y).[/tex]Therefore, point B(4,2) reflected over the x-axis:
[tex](4,2)\rightarrow(4,-2),[/tex]and then translated 3 units to the left has as image the following point:
[tex](4,-2)\rightarrow(4-3,-2)=(1,-2).[/tex]Answer:[tex]\begin{equation*} (1,-2). \end{equation*}[/tex]I need help question
as x approaches 8, x approaches 8
it's just 8
if 1/4 of the class is girls and one half of the girls in the class are wearing dresses what fraction of the class are girls with dresses one eighth 1/6 1/5 1/4
Given that one-fourth of the class are girls;
[tex]f(G)=\frac{1}{4}[/tex]And one half of the girls in the class are wearing dresses;
[tex]f(D)=\frac{1}{2}[/tex]The fraction of the class that are girls with dresses is;
[tex]\begin{gathered} f(G\cap D)=\frac{1}{4}\times\frac{1}{2} \\ f(G\cap D)=\frac{1}{8} \end{gathered}[/tex]Therefore, the fraction of the
If points P and Q lie in the interior of ∠ABC, then overline{PQ} lies in the interior of ∠ABC.True or false?
PQ is just the line segment that connects the points P and Q, so if both point are in the interior of and angle, the line segment connecting them has to be also in the interior of this angle, so true.
Sindy surveyed a group of students. The table represents the hours, h, they spent studying and their scores, s.What does the slope of the trend line equation s = 32.4h + 302.6 represent? For an increase of 1 h in study time the test score will increase by approximately 302.6.For an increase of 302.6 h in study time the test score will increase by approximately 1.For an increase of 32.4 h in study time the test score will increase by approximately 1.For an increase of 1 h in study time the test score will increase by approximately 32.4.
The slope of the trend line is 32.4, and it represents the change of s per 1 hour.
Then, as the slope is 32.4 it represents: For an increase of 1 h in study time the test score will increase by approximately 32.4