Step-by-step explanation:
if there is no typo, or there are no parts missing, then
-1 <= 2-j < -5
cannot have any solution, because already for the outside limits -1 < -5 is impossible. -1 is larger than -5 !
At the end of every month, Katie saves 20 percent of her take home pay after her taxes. If Katie is taxed at a 25 percent tax rate, which of the following expressions represents Katie’s total savings at the end of six months? A. 0.9S B. 1.5S C. 2.2S D. 2.8S
The correct answer is option A which is the expression will be 0.9S.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that:-
At the end of every month, Katie saves 20 percent of her take-home pay after her taxes. If Katie is taxed at a 25 percent tax rate,
The expression of the salary after six months will be calculated as:-
Let the gross salary is S
The net salary will be = 0.75S
Savings will be = 0.75 x 0.20 S = 0.15S
After six months the savings will be:-
Savings = 0.15 x 6 S
Savings = 0.9S.
Therefore the correct answer is option A which is the expression will be 0.9S.
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Find the minimum distance between the point (-3,2) and the line y = -x + 1
(Enter an exact answer with a square root.)
The minimum distance between the point(-3,2) and the line y = -x + 1 is [tex]\sqrt{2}[/tex] units.
What is a line segment?The line that joins two points on a cartesian plane is a line segment.
Analysis:
The formula for calculating distance between a line and a point is
d = [tex]\frac{Ax1 + By1 + c}{\sqrt{A^{2} + B^{2} } }[/tex]
where A = coefficient of x term of the line, B = coefficient of y in the line and C is the constant term of the line.
x1 and y1 are coordinates of the point.
for the line y = -x + 1 which is = y + x -1 = 0, A = 1, B = 1, C = -1, x1 = -3, y = 2
d = [tex]\frac{1(-3) + 1(2) + (-1)}{\sqrt{(-3)^{2} + 2^{2} } }[/tex]= [tex]\sqrt{2}[/tex] units
In conclusion, the distance between the point and the line is [tex]\sqrt{2}[/tex] units
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Please help me solve the x and y values in thes simultaneous equation;
Answer:
x = 3 or x = 1
y = 3 or y = -1
(x, y) = (3, 3)
(x, y) = (1, -1)
Step-by-step explanation:
5+√2/4+√8
can be written in the form
where r and s are both integers.
What are the values of r and s?
r-s√2/4
Answer:
r = 5 ; s = -9
Step-by-step explanation:
Radical simplification.First simplify √8 by
Prime factorize 8Make pairs of similar factorTake one factor out of every pair.[tex]\sf \sqrt{8}=\sqrt{2*2*2} = 2\sqrt{2}\\[/tex]
[tex]\sf \dfrac{5+\sqrt{2}}{4}+\sqrt{8}= \dfrac{5+\sqrt{2}}{4}+ 2\sqrt{2}[/tex]
Find LCM and simplify
[tex]\sf = \dfrac{5+\sqrt{2}}{4}+\dfrac{2\sqrt{2}*4}{1*4}\\\\ =\dfrac{5+\sqrt{2}+8\sqrt{2}}{4} \ {\bf Combine \ like\ terms} \\\\ = \dfrac{5+9\sqrt{2}}{4}\\\\[/tex]
[tex]\sf \boxed{r=5}\\\\\boxed{s =-9}[/tex]
Greg deposited $4000 into an account with a 9.8% annual interest rate, compounded semiannually. Assuming that no withdrawals are made, how long will it
take for the investment to grow to $4616?
Do not round any intermediate computations, and round your answer to the nearest hundredth.
The number of years it would take $4000 to grow to $4616 is 2.92 years.
How many years would it take the investment to have a value of $4616?When an amount earns compound interest compounded semi annually, it means that both the amount invested and the interest accrued increases in value twice yearly.
Number of years = (In FV / PV) / r
r = 9.8/2 = 4.90%FV = future value = 4616PV = present value = 4000(In 4616 / 4000) / 0.049 = 2.92 years
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If you apply the below transformations to the square root parent function,
F(x)=√x, what is the equation of the new function?
• Shift eight units left.
. Shift two units down.
O A. G(x) = VX- 2 - 8
B. G(x)=√x-8-2
C. G(x)=√x+8 - 2
OD. G(x)=√x-2 +8
Answer:
C. g(x) = sqrt(x+8)-2
Step-by-step explanation:
"Shift two units down" is easier to see in the equation because an up or down shift is just tacked right on to the end of the equation. So "shift DOWN 2" is a minus two on the end of the equation. This means that A and D are both NOT the answer.
Left and right shifts are the opposite of what you might expect. Left shift is a "+ anumber" and Right shift is
"- anumber" This is tucked in very close to the x, because a left or right shift is a change in the x-direction. Again left shift is "+ anumber", so in your question, "shift eight units left" shows in the equation as the plus8 beside the x.
So B is wrong and C is the answer.
100 POINTS
Give explanation also pls or reported
AB is a common tangent of circles C, D, E and F.
Suppose that AC = 12, DB = 9 and AE = BF = 3.
If the midpoint of EF is the center of a circle that is tangent to both circles E and F, what are the possible values for its radius?
Answer:
6√3 ±3 ≈ {7.392, 13.392}
Step-by-step explanation:
The length of AB is the long side of a right triangle with hypotenuse CD and short side (AC -BD). The desired radius values will be half the length of EF, with AE added or subtracted.
__
length of ABRadii AC and BD are perpendicular to the points of tangency at A and B. They differ in length by AC -BD = 12 -9 = 3 units.
A right triangle can be drawn as in the attached figure, where it is shaded and labeled with vertices A, B, C. Its long leg (AB in the attachment) is the long leg of the right triangle with hypotenuse 21 and short leg 3. The length of that leg is found from the Pythagorean theorem to be ...
AB = √(21² -3²) = √432 = 12√3
tangent circle radiiThis is the same as the distance EF. Half this length, 6√3, is the distance from the midpoint of EF to E or F. The radii of the tangent circles to circles E and F will be (EF/2 ±3). Those values are ...
6√3 ±3 ≈ {7.392, 13.392}
Answer:
6√3 ± 3
Step-by-step explanation:
AC is the radius of Circle C ⇒ radius = 12
DB is the radius of Circle D ⇒ radius = 9
Therefore, CD = AC + DB = 12 + 9 = 21
AE is the radius of Circle E ⇒ radius = 3
BF is the radius of Circle F ⇒ radius = 3
If AB is the common tangent of Circles C, D, E and F, then:
∠CAB =∠AEF = ∠DBA = ∠BFE = 90°
(as the tangent to a circle is always perpendicular its the radius).
Also AB = EF
To find the possible radii of a circle whose center is the midpoint of EF and is tangent to both circles E and F, we first need to find the length of EF (marked by x on the attached diagram).
CD is the hypotenuse of a right triangle with base equal to EF and a smaller leg of the difference between the radii of Circles C and D.
(Refer to the green shaded triangle on attachment 1)
Therefore, to find EF (x), use Pythagoras' Theorem a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
⇒ a² + b² = c²
⇒ 3² + x² = CD²
⇒ 3² + x² = (12 + 9)²
⇒ 9 + x² = 441
⇒ x² = 432
⇒ x = √432
⇒ x = 12√3
⇒ EF = 12√3
As the radius of Circles E and F is 3, the possible diameter of the circle with its center as the midpoint of EF is 6 less or 6 more than the length of EF.
⇒ diameter = EF ± 6
= 12√3 ± 6
As the radius is half of the diameter, the possible radii of a circle whose center is the midpoint of EF and is tangent to both circles E and F is:
⇒ radius = diameter ÷ 2
= (12√3 ± 6) ÷ 2
= 6√3 ± 3
(see attachments 2 and 3 → the possible circles are shown in orange)
What type of triangle has only two congruent sides?
Answer: A triangle that only has two congruent sides is called an isosceles triangle. Two equal sides and two equal angles.
Given that tan^2 theta=3/8,what is the value of sec theta?
Answer:
Sqrt (11/8)
Step-by-step explanation:
Sec^2 - Tan^2 = 1
- Tan^2 = 1 - Sec^2
Tan^2 = -1 + Sec^2
Tan^2 = 3/8
3/8 = -1 + Sec^2 Theta
1 + 3/8 = Sec ^2 Theta
11/8 = Sec^2 Theta
Sqrt ( 11/8) = Sec of theta
-- Gage Millar, Algebra 1/2 Tutor (Pending Pre-Calc Tutor)
What is the equivalent decimal to this fraction? 10/45 0.2 0.222222222... 0.232323232323... 0.181818181818...
Factorize the numerator and denominator, then simplify:
10/45 = (2×5)/(9×5) = 2/9
Now,
1/9 = 1/10 + 1/90
1/90 = 1/10 × 1/9 = 1/10 × (1/10 + 1/90) = 1/100 + 1/900
1/900 = 1/100 × 1/9 = 1/100 × (1/10 + 1/90) = 1/1000 + 1/9000
and so on, which is to say
1/9 = 1/10 + 1/100 + 1/1000 + …
or
1/9 = 0.111…
so that multiplying both sides by 2 gives
2/9 = 0.222…
A class sold tickets to their school play. Each of the 232323 students in the class sold 444 tickets. The cost of each ticket was \$7$7dollar sign, 7.
How much money did the class earn by selling tickets to the play?
\$
Answer:
the class earned $722059884
Step-by-step explanation:
because each person sold 444 tickets and there was 232323 students
=232323×444
=103151412
because 103151412 tickets were sold and a ticket cost $7
=103151412×7
=722059884
Rice Yield = 600 - 2.05 * Maximum Temperature, R-Squared = 0.05, Standard Error of Regression = 11.5.
(a) What is the interpretation on the coefficient on Maximum Tem perature in this regression? (2 Marks)
(b) If Average Maximum Temperature in a district during the growing season is 25◦C, what is the annual rice yield in that district? (1 Mark)
(c) How do you interpret the R-Squared coefficient in this regression? (1 Mark)
(d) A district had an Average Maximum Temperature during the growing season of 25◦C , and suppose it increased to 30◦C, What is the regression’s prediction for the change in this district’s Yearly Rice Yield? (1 Mark)
Answer:
Calculate it you will now the answer and im elementery school
If you help me you get a lot of points
Answer:
Step-by-step explanation:
#a
pattern 0 will include 4 reds in square
Because it's independent of pattern no
#b
Figure 1 has 4+4=8
Figure 2=4+8+2=14
Figure 3=4+12+3=19
The pattern n rule is
n²+3n+4So for 13th n
13²+3(13)+4169+39+4212squares#c
attached
y=x²+3x+4#d
Already given in c
The diameter of a circle is 94 cm.
By first calculating the radius, work
out the area of the circle.
2
Give your answer in cm² to 1 d.p.
[tex]\huge\boxed{Formula: r= \frac{d}{2}}[/tex]
Substitute the values according to the formula.
[tex]r=\frac{94}{2}[/tex]
[tex]\large\boxed{r=47 \: cm}[/tex]
Now, let's find the area.
[tex]\huge\boxed{Formula:a= \pi{r}^{2}}[/tex]
So, we'll have to multiply π, 47 and 47.
Substitute the values according to the formula.
[tex]a= \pi{47}^{2}[/tex]
[tex]a= 6939.778172 \: {cm}^{2}[/tex]
[tex]\large\boxed{a= 6939.8 \: {cm}^{2}(1 \: d.p)}[/tex]
Hence, the area of the given circle is 6939.8 square centimeters.
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the radius & area of the circle.
To find the [tex]\star\bf{radius}\star[/tex], we divide the diameter by 2:
[tex]\star~\bf{94\div2}[/tex]
[tex]\star~\bf{Radius=47}\star[/tex]
Now that we have the radius, let's compute the area! :)
///\\\///\\\///\\\///\\\///\\\////\\\///\\///\\\///\\\\///\\\///\\\///\\\////\\\///\\\///\\\///\\//\\\//\\
Calculating the Area
We can work out the area of a circle by using this formula:
[tex]\star\boxed{\pmb{A_{(circle)}=\pi r^2}}\star[/tex]
Where
[tex]\dag[/tex] A=Area of a circle
[tex]\dag[/tex] [tex]\pi =3.14...[/tex]
[tex]\dag[/tex] r=radius
Have you noticed the [tex]\large\pmb{^2}[/tex] next to r? This tells us that we should multiply the radius times itself.
Now it's time to substitute the values:
[tex]\star~\large\pmb{A=3.14\times47^{2}}\star[/tex]
Let's simplify it. The acronym PEMDAS will help us, and we won't make any mistakes in the Order of Operations! :)
Here's what it stands for:
P=Parentheses
E=Exponents
M=Multiplication
D=Division
A=Addition
S=Subtraction
2 is an exponent.
So what do you think we should do first?
[tex]\square[/tex] Square 47.
[tex]\square[/tex] Multiply 3.14 times 47 and then square.
That's right, we should square 47 first. :)
[tex]\star~\large\pmb{A=\pi \times2209}}\star[/tex]
Now, according to PEMDAS, we should multiply pi times 2209; after multiplying, we obtain:
[tex]\star~\large\pmb{A=6936.8\:cm^2}\star[/tex]
Remember, the area of any shape is measured in units squared.
[tex]\ddot\bigstar[/tex] Remember this...
[tex]\fbox{\bf{The\;area\;of\;any\;shape\;is\;measured\;in\;units\;squared}}[/tex]
Hope this helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
[tex]\bigstar\footnotesize\pmb{M^ar_ib^el\;Peri}[/tex]
P(A1) = .20, P(A2) = .40, P(A3) = .40, P(B1 | A1) = .25, P(B1 | A2) = .05, and P(B1 | A3) = .10. Use Bayes’ theorem to determine P(A3 | B1).
Answer:The result follows from manipulating the conditional probability. By definition,
By the law of total probability,
So we have
Step-by-step explanation:
P(A|B) = P(B|A)×P(A)/P(B)
so, in our case
P(A3|B1) = P(B1|A3)×P(A3)/P(B1) = 0.1×0.4/P(B1)
I assume that the problem definition means that A1, A2, A3 are independent and not overlapping events (hence their sum is 1). and therefore, B1 can only happen after A1 or after A2 or after A3. there is no other possibility for B1 to happen.
so,
P(B1) = P(B1|A1) + P(B1|A2) + P(B1|A3) =
= 0.25 + 0.05 + 0.1 = 0.4
therefore,
P(A3|B1) = P(B1|A3)×P(A3)/P(B1) = 0.1×0.4/0.4 = 0.1
how do I Simplify 4+9x2÷3-1
Step-by-step explanation:
Step 1: Simplify
[tex]4+9x^2/3 - 1[/tex]
[tex]=4+3x^2+-1[/tex]
Step 2: Combine Like Terms:
[tex]= 4+3x^2+1-1[/tex]
[tex]= (3x^2)+(4+-1)[/tex]
Answer: [tex]= 3x^2+3[/tex]
Explanation in words (Short Form)
- The first step is to use the formula and simplify it. So first we will Rewrite the division as a fraction.
- The second step is to Cancel the common factor of 9 and 3. Then Factor 3 out of 3. After that Cancel the common factor.
- The third step is to divide [tex]3x^2[/tex] by 1. Then at the end, subtract 1 from 4. The answer will result as [tex]3x^2+3[/tex]
Answer:
[tex]=3x^2+3[/tex]
Hope this helps.
A group surveyed a mix of people below and above 40 years old about whether or not they visit a dentist once a year. This table gives the survey results.
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 8 22
Above 40 17 13
Which table shows the relative frequency of people above 40 years old who do not visit a dentist once a year? Round your answers to the nearest hundredth.
A.
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 0.32 0.68
Above 40 0.63 0.37
B.
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 0.35 0.65
Above 40 0.68 0.32
C.
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 0.37 0.63
Above 40 0.53 0.47
D.
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 0.27 0.73
Above 40 0.57 0.43
The frequency table that shows the relative frequency of people older than 40 and don't visit the dentist is:
D. Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 0.27 0.73
Above 40 0.57 0.43
What is the relative frequency required?The relative frequency of those older than 40 and don't go annually to a dentist can be found as:
= Number of over 40 who don't go to dentist / Total of those over 40 surveyed
Solving gives:
= 13 / (17 + 13)
= 13 / 30
= 0.43
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Answer:
Its D, I got it right on a test :)
Step-by-step explanation:
19 Which figure(s) below can have a triangle as a two-dimensional cross
section?
I. cone
II. cylinder
III. cube
IV. square pyramid
(1) I, only
(2) IV, only
(3) I, II, and IV, only
(4) I, III, and IV, only
The figures that can have a triangle as a two-dimensional cross section are (4) I, III, and IV, only
How to determine the figures?The cross-section of three-dimensional figures are as a result of slicing the figure along its axis.
When the cube is sliced with its plane, it gives a triangle faceWhen a cone is sliced vertically, it gives a triangle faceOne of the faces of a square pyramid is a triangle; so it has a triangle faceHence, the figures that can have a triangle as a two-dimensional cross section are (4) I, III, and IV, only
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What slope would make the lines parallel
Answer:
3
Step-by-step explanation:
Parallel lines are a fixed distance apart and will never meet, no matter how long they are extended. Lines that are parallel have the same gradient . The equations above, y = 3x -2 and y = ? x +3 have the same gradient of 3 if they are to be parallel
Hope you understood and this helped and have a good day
in which situation do the qaultities cobine to make 0
Which statement correctly compares the function shown on
this graph with the function y = 4x + 2?
(8.2 x 10^4) + (9.7 x 10^5)
Answer:
1.052 × 10⁶
Step-by-step explanation:
82,000 + 970,000 = 1,052,000
Answer:
[tex]\left(8.2\cdot \:10^4\right)+\left(9.7\cdot \:10^5\right)=1,052,000[/tex]
Step-by-step explanation:
[tex]\left(8.2\cdot \:10^4\right)+\left(9.7\cdot \:10^5\right)\\=8.2\cdot \:10^4+9.7\cdot \:10^5\\\\\rightarrow 10^4 = 10000\\= 8.2 \cdot 10000\\= 82000\\\rightarrow 10^5 = 100000\\= 9.7 \cdot 100000\\= 970000[/tex]
[tex]970000 + 82000 = 1052000[/tex]
in the figure, angle D measures 31° and angle A measures 27
The measurement of angle B Is ?The measurement of angle F is?
The acute angles of a right triangle are complementary, so:
[tex]m\angle B=90-27=\boxed{63^{\circ}}\\m\angle F=90-31=\boxed{59^{\circ}}[/tex]
please help i need to turn this in!!!
Answer:
a. $3150
b. $3307.50, $3472.875
c. B(n) = 3000(1.05)^t
Step-by-step explanation:
just a disclaimer i havent done interest in a while so this might not be right
also im assuming this is compound interest
a. P = original amount; r = interest percentage, x = amount of total money
x = P(1 + (r/100)) = 3000(1 + 0.05) = 3150
b. x = 3000(1.05)^2,3 = 3307.5, 3472.875
c. B(n) = P(1+(r/100)^t for t in years. plug in the values to get B(n) = 3000(1.05)^t
pls help plsssssssssssssssssssssssssssssssssssssssssss ASAP
If Mr. Price adds two more CDs that are 38 minutes and 40 minutes, the third quartile would increase.
What is the impact of adding two more CDs?A box plot is used to study the distribution and level of a set of scores. The two whiskers represent the minimum and maximum value.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.
When the two CDs are added, the median would decrease. The first quartile and the third quartile would increase. The interquartile range would increase.
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Two six-sided dice are rolled. Using the sample space for rolling two dice shown in the figure below, find the probability that the sum of the dice is either 4 or 7. Give your answer as a reduced fraction.
Answer:
Step-by-step explanation:
There are 36 ways 2 dice can be thrown. Sometimes colors are used to tell the difference between the dice.
36 comes from 6*6
Suppose you have 2 dice 1 blue and the other white
Blue White
1 1
2
3
4
5
6
There's 6 ways that have been thrown. Then you go to the blue dice being 2. You get six more. Then 3 gives you six more 4 gives you another six. and so on. The whole procedure adds to 36
you can throw a four 3 ways
Blue white
1 3
3 1
2 2
You can throw 7 six ways
Blue white
1 6
6 1
2 5
5 2
3 4
4 3
So of the 36 ways to throw the dice 9 will successful. (6 + 3)
Answer: 9/36 = 1/4 times you will be successful
help me with this problem please i’m confused
Answer:
3rd
Step-by-step explanation:
If you know about linear eq. it's just a simple rule no worry
If the simple interest on $4000 for 2 years is $400, then what is the interest rate?
Step-by-step explanation:
the answer is 5 percentage because the formula is 100 * 400 over 4000 * 2
In which table does yvary directly with x?
The table in which y varies directly with x is table C.
What is direct variation?
When a variable varies directly with another variable, it means that as one variable increases, the other variable also increases.
The equation that is used to represent direct variation is:
y = kx
Where y is the constant of proportionality
In table c, k is equal to 26
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An automobile manufacturer produces production parts with 98% accuracy. What is the probability that in a production run of 25 parts, at most 2 are found to be defective?
An automobile manufacturer produces production parts with 98% accuracy. the probability is mathematically given as
P(X\leq2) = 0.9868
What is the probability that in a production run of 25 parts, at most 2 are found to be defective?Generally, the equation for the probability is mathematically given as
[tex]P(X\leq2) = P(X=0) + P(X=1) + P(X=2)[/tex]
Therefore
[tex]P(X=0)=\binom{25}{0}* 0.98^{25}* 0.02^{0}=1* 0.6035* 1\\\\P(X=0)=0.6035[/tex]
Hence
P(X=1)=0.3079
P(X=0)=0.07554
In conclusion, bringing the equation into view
[tex]P(X\leq2) = P(X=0) + P(X=1) + P(X=2)[/tex]
[tex]P(X\leq2) = 0.6035 +0.3079 + 0.07554[/tex]
P(X\leq2) = 0.9868
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