Answer:
9 and 1 respectively
Step-by-step explanation:
|2(-3)-5| = |-9| = 9
|2(2)-5| = |1| = 1
the vertical lines represents absolute value, this just mean that any negative values are then turned into their positive counterparts.
What is the value of sec 3pi/2 in simplest form with a rational denominator?
The given expression is
[tex]sec\frac{3\pi}{2}[/tex]Since sec is the opposite of cosine, then
[tex]sec\frac{3\pi}{2}=\frac{1}{cos\frac{3\pi}{2}}[/tex]Since the value of cos(3pi/2) is 0, then
[tex]\begin{gathered} cos\frac{3\pi}{2}=0 \\ \\ sec(\frac{3\pi}{2})=\frac{1}{cos\frac{3\pi}{2}}=\frac{1}{0} \end{gathered}[/tex]Since 1/0 is an undefined value, then
The answer is undefined
C IS BETWEEN A AND D, B IS THE MIDPOINT OF AC . IF BD =15 AND BC= 7, FIND AD
BD= 12
BC=7
Is this from a graded quiz?
pls solve this question properly
Answer:
∡BOA ≅ ∡DOC
Step-by-step explanation:
Given a circle O with congruent chords BA and DC, you want the relation between angles BOA and DOC.
CongruenceAll of the radii of circle O are congruent. That means BO≅AO≅DO≅CO. The chords BA and DC are marked as congruent. This means ∆BOA and ∆DOC are congruent by the SSS postulate.
Corresponding parts of congruent triangles are congruent, so ...
∡BOA ≅ ∡DOC
Find the critical value (tα/2) for a 90% confidence interval if the sample size is 15. Round your answer to three decimal places.
tα/2 =
The critical value of tα/2 for a 90% confidence interval for the sample size 15 is 1.761.
Given, sample size=15
Confidence interval= 90%.
To find the critical value we have to first find alpha, by subtracting 90 from 100.
= 100%-90%
=1-0.9
=0.1
α=0.1
α/2=0.05
Next, we have to find the degrees of freedom(df) by using the formula n-1.
=15-1
df=14
Calculate tα/2 by using t-distribution with degrees of freedom 14 and α/2 = 0.05 as right-tailed area.
From the table we get the critical value for tα/2 as 1.761.
Therefore, the critical value for a 90% confidence interval with sample size 15 is 1.761.
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Im not the best at word problems please help.Frank knows that his first four test grades were 74, 76, 77, and 84. Use the formula x‾=x1+x2+…+xnn to find Frank's grade on the fifth test if his test average is 80.6.
Given:
Frank knows that his first four test grades were 74, 76, 77, and 84
We will find Frank's grade on the fifth test if his test average is 80.6.
So, let the fifth grade = x,
The average is the sum of the grades over the number of the grades
So,
[tex]\frac{74+76+77+84+x}{5}=80.6[/tex]Solve the expression to find x:
[tex]\begin{gathered} 74+76+77+84+x=5\cdot80.6 \\ 311+x=403 \\ x=403-311=92 \end{gathered}[/tex]So, the answer will be: the fifth grade = 92
You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ = 50.2 . You would like to be 90% confident that your estimate is within 1.5 of the true population mean. How large of a sample size is required?
The required sample size of the given estimate is 3030.65.
Given that,
The population standard deviation is approximately σ = 50.2. You would like to be 90% confident that your estimate is within 1.5 of the true population mean.
Statistics is the study of mathematics that deals with relations between comprehensive data.
Here,
For the 90% confidence the value of the z = 1.645
Now the sample size is given as,
n = [z × σ/1.5]²
Substitute values in the above equation,
n = [1.645×50.2/1.5]²
n = 3030.65
Thus, the required sample size of the given estimate is 3030.65.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The required solution of the inequality on the number line is represented as x>20 .
Any monotonically rising function can, by definition, be applied to both sides of an inequality without destroying the inequality connection (provided that both of the expressions are in the domain of that function).
–3(2x – 5) < 5(2 – x)
-6x+30 < 10-5x
-6x+5x<-20
-x<-20
x>20 (x∈R)
The inequality relation is flipped when a monotonically decreasing function is applied to both sides of an inequality. In the equations for the adding inverse and multiple inverse for positive numbers, a monotonically decaying function is utilized.
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according to City high school's alumni records 375 students graduated in college in 2001 are these graduates 176 were female 100 and 47 of whom were accepted into college of the male graduate 100 were accepted to college.A) what is the probability that a 2001 graduate of City high School was accepted into collegeB) what is the probability that 2001 graduate of City high School was not a female C)what is the probability that a 2001 graduate of City high School was accepted into college or maleD) what is the probability of being a female given you were accepted into college.
We are asked to determine probabilities from a population of high school graduates. Let's remember that probability is defined as the quotient of desired events and the number of total events.
a) what is the probability that a 2001 graduate of City High School was accepted into college
To determine the probability we need to find the quotient of the number of students that were accepted into college and the total number of students. The total number of students accepted into college is 145 female plus 100 males, therefore, the probability is:
[tex]P(a)=\frac{145+100}{375}=\frac{245}{375}=0.653[/tex]Therefore, the probability is 65.3%.
b)what is the probability that 2001 graduate of City high School was not a female
To do this we will use the fact that the sum of the probabilities that a student is a female plus the probability that the student is not a female must be equal to 1.
[tex]P(\text{female)}+P(\text{not female)=1}[/tex]Therefore, solving for the probability that the student is not a female we get:
[tex]P(\text{not female)=1-P(female)}[/tex]The probability that the student is female is the quotient between the number of female students and the total number of students, therefore:
[tex]\begin{gathered} P(\text{not female)=1-}\frac{176}{375} \\ \\ P(\text{not female)=1-0.461} \\ P(\text{not female)=0.539} \end{gathered}[/tex]Therefore, the probability that the student is not a female is 53.9%.
c) what is the probability that a 2001 graduate of City high School was accepted into college or male
To determine this probability we need to have into account that the probability of event A or event B happening is the sum of both probabilities minus the probability of both events happening at the same time, therefore:
[tex]P(\text{accepted or male)=P(accepted)+P(male)}-P(\text{accepted and male)}[/tex]Replacing the probabilities we get:
[tex]P(\text{accepted or male)=}0.653+\frac{375-176}{375}-\frac{100}{375}[/tex]Solving the operations:
[tex]\begin{gathered} P(\text{accepted or male)=0.653+0.53-0.267} \\ P(\text{accepted or male)=0.916} \end{gathered}[/tex]Therefore, the probability that a student is accepted or male is 91.6%
d) what is the probability of being a female given you were accepted into college.
The probability of event A given event B is given by the following formula:
[tex]P(A\parallel B)=\frac{P(AandB)}{P(B)}[/tex]In this case, we have:
[tex]P(female\parallel accepted)=\frac{P(\text{female and accepted)}}{P(accepted)}[/tex]Replacing the probabilities:
[tex]\begin{gathered} P(female\parallel accepted)=\frac{\frac{147}{375}}{0.653} \\ \\ P(female\parallel accepted)=\frac{0.392}{0.653} \\ \\ P(\text{female}\parallel accepted)=0.6 \end{gathered}[/tex]Therefore, the probability is 60%.
Julie is given two points, (x,y) and (w,z). Which process can she use to find the distance between the points?
One option is to use the distance formula.
In this case, this is what Julie would be working with:
[tex]d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(x-w)^2+(y-z)^2}\\\\[/tex]
If Julie knew the values of x, y, w, and z, then she could find a numeric result for the distance (d).
Find csco, cose, and tan , where is the angle shown in the figure.Give exact values, not decimal approximations.
Let 'a' represent the unknown side of the triangle.
To solve for the unknown side, we will apply the Pythagoras theorem.
[tex]a^2=b^2+c^2^{}[/tex][tex]\begin{gathered} b=4 \\ c=5 \end{gathered}[/tex][tex]\begin{gathered} a^2=4^2+5^2 \\ a=\sqrt[]{16+25} \\ a=\sqrt[]{41} \end{gathered}[/tex]Let solve for cscθ
[tex]\begin{gathered} \csc \theta=\frac{1}{\sin \theta} \\ \sin \theta=\frac{4}{\sqrt[]{41}} \\ \text{Therefore,} \\ \csc \theta=\frac{1}{\frac{4}{\sqrt[]{41}}}=\frac{\sqrt[]{41}}{4} \end{gathered}[/tex]Let us solve for cosθ
[tex]\cos \theta=\frac{5}{\sqrt[]{41}}[/tex][tex]\begin{gathered} \frac{5}{\sqrt[]{41}} \\ \text{Rationalising} \\ \frac{5}{\sqrt[]{41}}\times\frac{\sqrt[]{41}}{\sqrt[]{41}}=\frac{5\sqrt[]{41}}{41} \end{gathered}[/tex][tex]\cos \theta=\frac{5\sqrt[]{41}}{41}[/tex]Let us solve for tanθ
[tex]\tan \theta=\frac{4}{5}[/tex]Can I get help in #5 ? I don’t get it
Step 1
The selection formula is;
[tex]\begin{gathered} ^nc_r=\frac{n!}{r!(n-r)!} \\ n=10 \\ r=5 \end{gathered}[/tex][tex]=\frac{10!}{5!(10-5)!}=\frac{3628800}{120(120)}=252\text{ groups}[/tex]Answer; 252 groups
help me please if you can i need to know the equation
Following the instructions provided, we shall use a graphing calculator (Desmos) to determine the equation of the circle shown by the "colorful people."
The first step is to determine the radius which we can observe from the circle itself, whose diameter spans from 0 units to 10 units along the x-axis. The radius therefore is 5 units (half of the diameter).
Observe also that the center has now moved away from the origin (0, 0), and if we move the slider very carefully for h, that would be 5 units away from the origin towards the right (along the x-axis), andk would be 7 units away from the origin) towards the bottom (along the y-axis).
After following these steps, we can replicate the circle given in the question and if we now substitute the values of h, k and r into the equation of a circle, we would end up with;
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{Where;} \\ h=5,k=-7,r=5 \\ \text{The equation becomes;} \\ (x-5)^2+(y-\lbrack-7\rbrack)^2=5^2 \\ (x-5)^2+(y+7)^2=25 \end{gathered}[/tex]Kim's room is an 11 ft by 12 ft rectangle. How many square feet of carpeting does she need to buy to cover the entire floor?
In order to calculate the area of carpet needed to cover the entire floor, we just need to calculate the area of the room.
The area of a rectagle is calculated by the product of its dimensions, so we have:
[tex]\text{Area}=11\cdot12=132\text{ ft2}[/tex]So the area of carpet needed is 132 square feet.
Use 3.14 for pi or the pi button and round to the nearest hundredth. The volume of the cone?
Given:-
[tex]r=4.5,h=9[/tex]To find the volume of cone.
So the volume formula for cone is,
[tex]v=\pi r^2\frac{h}{3}[/tex]Substituting we get,
[tex]\begin{gathered} v=3.14(4.5)(4.5)(\frac{9}{3}) \\ v=3.14(4.5)(4.5)(3) \\ v=190.755 \end{gathered}[/tex]So the required solution is 190.76
Bill bought a table on sale for $558. This price was 28% less than the original price,What was the original price?
For the new price to be 28% less than the original price then, therefore, the original price is definitely more than the new price
Let the original price be
[tex]x[/tex]the new price given is
[tex]\text{ \$558}[/tex]It means that the percentage decrease is
[tex]28\text{ \%}[/tex]The formula for percentage decrease is
[tex]\text{percentage decrease=}\frac{\text{original price-new price}}{\text{original price}}\times100\text{ \%}[/tex]By substitution, we will have
[tex]\begin{gathered} 28=\frac{x-\text{ \$558}}{x}\times100 \\ 28x=100x-55800 \\ 55800=100x-28x \\ 72x=55800 \\ \frac{72x}{72}=\frac{55800}{72} \\ x=\text{ \$775} \end{gathered}[/tex]Therefore,
The original price = $775
The graph y= f(x) is shown. Translate it to get the graph of y = f(x-2)
The translation of two units right of the graph of y = x is graphed at the end of the answer.
TranslationTranslation is a transformation to the graph of a function or of a figure that keeps everything such as orientation and inclination stable, changing only the position of the graph.
The translations are movements to left, right, up or down, and each movement is represented as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.In this problem, the definition of the translation is given as follows:
y = f(x - 2).
Hence a = 2, and the function is shifted right 2 units.
Considering function y = x, the translated function is:
y = f(x - 2) = x - 2.
(each instance of x in the function is replaced by x - 2).
The graph of the two functions is shown at the end of the answer, which x - 2 being a shift right of 2 units of f(x).
Missing InformationThe function is not given, hence we suppose that it is of y = x.
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I need help with this question but no one is helping me! Can someone please help me
Answer:
when rounding the answer it shouldn't be the exact answer so add or multiply then once you find your product round it off and add a decimal
please help with this practice question, thank you
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: .25x + 75.00 = C(x)
Step-by-step explanation:
Hi, can you please help me with my math? Please help me please that's all I'm asking and thank you so much.Good evening g, thanks for helping meHi, can you please help me with my math? Please help me please that's all I'm asking and thank you so much.The problem is 7.Can you please help and thanks 7. The two lines y=4x+5 and y= 4x-2 are parallel because their slopes are equal (both equal to 4).What happens when you try to algebraically solve for their intersection point?
No solution
Explanation:y = 4x + 5
y = 4x - 2
Solving algebraically:
equate both equations
y = y
4x + 5 = 4x - 2
collect like terms:
4x - 4x = - 2 - 5
0 = -7
When the right hand side is not the same as the left hand side equation, it is a no solution.
Their intersection point gives no solution
there are about 6*10^24 molecules in a litre of water. it is estimated that a person drinks about 2.2 *10^3 litres of water a year. how many molecules of water does a person drink in a year?
Based on the concept of multiplication, the amount of molecules consumption of water does a person drink in a year is 1.32 x 10²⁸.
Molecules:
A molecules is the group of two or more atoms linked together by sharing electrons in a chemical bond
Given,
There are about 6 x 10²⁴ molecules in a liter of water. it is estimated that a person drinks about 2.2 x 10³ liters of water a year.
Here we have to find the amount of molecules consumption of water does a person drink in a year.
To find the total amount of molecules consumption for the year we have to use the following formula,
Total molecules consumption per year = amount of water x molecules.
Here we know the values of the following,
Water consumption per year = 2.2 x 10³ liters
Molecules of one liter water = 6 x 10²⁴
Apply the values on the formula, then we get,
=> total molecules consumption = (2.2 x 10³) x (6 x 10²⁴)
=> (2.2 x 6) x (10³ x 10²⁴)
=> 13.2 x 10³⁺²⁴
=> 13.2 x ²⁷
It can be further simplified as,
=> 1.32 x 10²⁸
Therefore, the amount of molecules consumption of water does a person drink in a year is 1.32 x 10²⁸.
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what is 10 divided by 3 1/3
Answer:
10 divided by 3 1/3 is;
[tex]3[/tex]Explanation:
We want to divide 10 by 3 1/3;
[tex]10\div3\frac{1}{3}[/tex]Firstly, let us convert the mixed fraction to improper fraction;
[tex]\begin{gathered} 10\div\text{ }\frac{3(3)+1}{3} \\ =10\text{ }\div\text{ }\frac{10}{3} \end{gathered}[/tex]Then we can proceed to divide;
[tex]\begin{gathered} 10\text{ }\div\text{ }\frac{10}{3} \\ 10\times\frac{3}{10} \\ =\frac{30}{10} \\ =3 \end{gathered}[/tex]Therefore, 10 divided by 3 1/3 is;
[tex]3[/tex]What is the quotient of 7.7 x 10^8 and 5.5 x 10^2 expressed in
scientific notation?
The quotient of 7.7 x 10^8 and 5.5 x 10^2 expressed in scientific notation is 1.4x10^6.
What is quotient?
A quotient in mathematics is the amount created by dividing two numbers. The term "quotient" is used frequently in mathematics and is used to describe the integer component of a division (when Euclidean division), as well as a fraction or a ratio (when proper division). A quotient in the second sense is only the proportion of a dividend to its divisor.
Lets calculate the quotient for the value given in question:
[tex]7.7 \times 10^8[/tex]
[tex]5.5 \times 10^2[/tex]
Now we divide the 7.7 by 5.5
[tex]\frac{7.7}{5.5} = 1.4[/tex]
we get value 1.4.
on dividing [tex]\frac{10^8}{10^2}[/tex] we get, [tex]10^6[/tex]
Combining both the value, we get
quotient = [tex]1.4 \times 10^6[/tex]
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express 952 in scientific notation and please show the work
We are asked to express 952 in scientific notation
The scientific notation is given by
[tex]952=9.52\times10^2[/tex]The number 952 has the decimal point at the end, so we move this decimal point to the left until there is only one digit is left (9 in this case) and then count the number of times we moved.
In this case, we moved 2 times so the exponent (power) is 2
The sign of exponent is positive when we move to the left (like in this case)
The sign of exponent is negative when we move to the right.
Please help with math question
Answer:
x-intercept is at (18, 0)
y-intercept is at (0, 360)
If F(X) = 5x-7 and G(X)= -2x+9, what is G(F(X))?O A. -10x +23O B. -10X2 +59x-63O C. -10x+38O 10XD. 10x7 - 59x+63
f(x) = 5x - 7
g(x) = -2x + 9
g(f(x)) = -2(5x -7) + 9 = -10x + 14 + 9 = -10x + 23
g(f(x)) = -10x + 23
Answer:
Option A: -10x + 23
Since 12:00 am., a cold front has caused the tempurature in a particular city to decrease at a constant rate. At 2:00 a.m., the tempurature was 54 degrees Farenheit, and at 5:00 a.m., the tempurature was 45 degrees Fahrenheit. Which of the following statements is correct?
A. The tempurature at 12:00 a.m. was 57 degrees Fahrenheit.
B. The tempurature at 12.00 a.m was 60 degrees Fahrenheit.
C. The tempurature at 12:00 a.m was 63 degrees Fahrenheit.
D. The tempurature is decreasingn at a rate of 9 degrees Fahrenheit per hour.
Answer: B.
Step-by-step explanation: First, you find the difference between 2 and 5 =( 3 ), and 54 and 45 ( -9 ). Meaning the unit rate is -3. (-9/3 = -3)
The difference between 12:00 am and 2:00 am is 2 hours meaning 2 x 3 is 6. 54 + 6 = 60 meaning at 12:00 am it was 60 degrees Fahrenheit.
Wade and Ida are salespeople who earned the same amount this week, although Ida made 4 more sales than Wade. Wade earns a base of $153 plus $22 per sale. Ida earns a base of $17 plus $24 per sale. Write the equation for the number of sales Wade made this week
Answer:
y = 24x + 17 20
Step-by-step explanation:
Firstly, let's say that 153 and 17 are both the y-intercepts of their respective equations, while 22 and 24 are the slope. With this we can create the following set of equations:
y = 24x + 17
y = 22x + 153
So your answer would be y = 24x + 17
Now let's find the sales answer!
Since we know that Ida made 4 more sales than Wade this week, we could say:
y = 24(x+4) + 17
y = 22x + 153
Now since we know that they earned the same amount we can do the following:
24(x+4) + 17 = 22x + 153
Simplify...
24x + 96 + 17 = 22x + 153
Simplify again:
24x + 113 = 22x + 153
subtract 22x and 113 from both sides...
2x = 40
Then:
x = 20
So this means that Wade made 20 sales this week!
So let's check if we are right:
Now that we know that x = 20, we need to plug it into Wade's equation!
y = 22(20) + 153
y = 440 + 153
y = 593
Wade made $593 this week!
To check if we are right, let's plug it into Ida's equation:
y = 24x + 113
y = 24(20) + 113
y = 480 +113
y = 593
Ida also made $593 this week!
MEANING we are right!
I hope I helped :P
Juan's father deposited $1500 in the bank as a graduation gift for juan. The bank pays a compound interest rate of 12% compounded annually. What is Juan's balance after 4 years
Find the equation of the line whose slope is 1/6 passing through the point (-9, 3)
The equation of the line whose slope is 1/6 passing through the point (-9, 3) is -x - 6y - 27 = 0
What is slope formula ?To determine a line's inclination or steepness, use the slope formula. By calculating the ratio of the change in the y-axis to the change in the x-axis, it may be used to calculate the slope of any line. A line's slope is determined by how its "y" coordinate changes in relation to how its "x" coordinate changes.
Given slope of equation m =[tex]\frac{1}{6}[/tex]
A point on line (x₁,y₁) = (-9,3)
(y-y₁)= m (x-x₁)
(y-3) = [tex]\frac{1}{6}[/tex] ( x − (-9))
y-3= [tex]\frac{1}{6}[/tex] (x+9)
6(y-3) = x+9
6y - 18 = x +9
-x - 6y - 27 = 0
This is the equation of line
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