Answer:
2[tex]\sqrt{34}[/tex]
Step-by-step explanation:
Calculate the distance (d) using the distance formula
d = √(x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 2, 4) and (x₂, y₂ ) = (4, - 6)
d = [tex]\sqrt{(4+2)^2+(-6-4)^2}[/tex]
= [tex]\sqrt{6^2+(-10)^2}[/tex]
= [tex]\sqrt{36+100}[/tex]
= [tex]\sqrt{136}[/tex] = [tex]\sqrt{4(34)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{34}[/tex] = 2[tex]\sqrt{34}[/tex]
What are the first two terms of the sequence defined recursively by the formula ^an=(^an-1)^2, when ^a4=1604?
Answer:
The first two terms are √2 and 6.
Step-by-step explanation:
a3^2+4=1604
a3=40
a2^2+4=40
a2=6
a1^2+4=6
a1=√2
The first two terms are approximately a1 ≈ 2.52 and a2 ≈ 6.33.
First Two Terms of the Sequence
To find the first two terms of the sequence defined recursively by the formula an = (an-1)2, given that a4 = 1604, we need to work backwards.
Step-by-Step Explanation:
Given: a4 = 1604.Since an = (an-1)^2, we take the square root of 1604 to find a3:Therefore, the first two terms of the sequence are approximately a1 ≈ 2.52 and a2 ≈ 6.33.
Helpppp me pleaseeeeeee
Answer:
my bad if im wrong but im pretty sure its b
Step-by-step explanation:
gradient answer it for bare points
Gradient is the slope of the line.
Use two points of the graphed line to find the slope, which is the change in Y over the change in x.
I'll use the points (4,0) and (6,8)
Slope = (8-0) / 6/4) = 8/2 = 4
The gradient is 4
For a group experiment, your science class measured the fine-particulate
concentrations in the air at random places around campus, and estimated a
sample average of 12 ug/m3 (micrograms per cubic meter). If 196 readings
were taken, and the standard deviation of the sample measurements was
3.5 pg/m3, you are 99.7% confident that actual concentration of fine
particulates at the school is
Answer:
The 99.7% confidence interval for the mean here is
[tex]\rm (11.2, 12.8)\; \mu g\cdot m^{-3}[/tex].
Step-by-step explanation:
The data in this question comes from random samples. In other words, the true population data are not known. Assume that both the sample average and the sample stdev are unbiased estimates for the population mean and stdev.
The sample size 196 is sufficient large, such that the central limit theorem will apply. By the central limit theorem, the distribution of the mean (as well as the sum) of a sufficiently large samples resembles normal distributions. However, since stdev is only an estimate, the confidence interval can only be found using the Student's t-distribution.
What is the confidence interval for the mean of a random variable that follows the t-distribution?
[tex]\displaystyle \left(\bar{x} - t\cdot \frac{s_{n-1}}{\sqrt{n}}, \; \bar{x} + t\cdot \frac{s_{n-1}}{\sqrt{n}}\right)[/tex],
where
[tex]\bar{x}[/tex] is the unbiased estimate of the population mean (a.k.a sample mean.) For this question, [tex]\bar{x} = 12[/tex]. [tex]s_{n-1}[/tex] is the unbiased estimate of the standard deviation (the square root of variance) of the population. For this question, [tex]s_{n-1} = 3.5[/tex].[tex]n[/tex] is the sample size. For this question, [tex]n = 196[/tex].What is not given is
[tex]t[/tex], the test statistics of the t-distribution. This value depends on the confidence level of the estimate (99.7% in this case.)Start by determining the degree of freedom [tex]df[/tex] of [tex]t[/tex]. The degree of freedom for a one-variable estimate is usually equal to [tex]n -1[/tex] (that is: sample size minus one.) For this question, [tex]n = 196[/tex] so [tex]df = 196 - 1 = 195[/tex].
If [tex]T[/tex] represent a random variable that follows the [tex]t_{195}[/tex]-distribution, the value of t shall ensure that
[tex]P(-t \le T \le t) = \text{Confidence Interval} = 0.997[/tex].
The t-distribution is symmetric. As a result,
[tex]\displaystyle P(T > t) = 0.997 + \frac{1}{2}\times (1 - 0.997) = 0.9985[/tex].
Find the value of [tex]t[/tex] either with a t-distribution table or with technology. Keep in mind that for this question, [tex]df = n - 1 = 195[/tex].
[tex]t \approx 3.00549[/tex].
Apply the formula for the confidence interval:
[tex]\displaystyle \left(\bar{x} - t\cdot \frac{s_{n-1}}{\sqrt{n}}, \; \bar{x} + t\cdot \frac{s_{n-1}}{\sqrt{n}}\right)[/tex].
Lower bound:
[tex]\displaystyle \bar{x} - t\cdot \frac{s_{n-1}}{\sqrt{n}} &= 12 - 3.00549\times \frac{3.5}{\sqrt{196}}\approx 11.2[/tex].
Upper bound:
[tex]\displaystyle \bar{x} + t\cdot \frac{s_{n-1}}{\sqrt{n}} &= 12 + 3.00549\times \frac{3.5}{\sqrt{196}}\approx 12.8[/tex].
In other words, the 99.7% confidence interval for the actual concentration is [tex]\rm (11.2, 12.8)\; \mu g\cdot m^{-3}[/tex].
Drag the tiles to the correct boxes to complete the pairs. Match each inequality to the number line that represents its solution. x – 99 ≤ -104 x – 51 ≤ -43 150 + x ≤ 144 75 < 69 – x
Answer:
The four answers in the attached figure
Step-by-step explanation:
Part 1) we have
[tex]x-99\leq-104[/tex]
Solve for x
Adds 99 both sides
[tex]x-99+99\leq-104+99[/tex]
[tex]x\leq-5[/tex]
The solution is the interval ----> (-∞, -5]
All real numbers less than or equal to -5
In a number line, the shaded area at left of x=-5 (close circle)
Part 2) we have
[tex]x-51\leq-43[/tex]
Solve for x
Adds 51 both sides
[tex]x-51+51\leq-43+51[/tex]
[tex]x\leq 8[/tex]
The solution is the interval ----> (-∞, 8]
All real numbers less than or equal to 8
In a number line, the shaded area at left of x=8 (close circle)
Part 3) we have
[tex]150+x\leq144[/tex]
Solve for x
Subtract 150 both sides
[tex]150+x-150\leq144-150[/tex]
[tex]x\leq -6[/tex]
The solution is the interval ----> (-∞, -6]
All real numbers less than or equal to -6
In a number line, the shaded area at left of x=-6 (close circle)
Part 4) we have
[tex]75<69-x[/tex]
Solve for x
Subtract 69 both sides
[tex]75-69<69-x-69[/tex]
[tex]6<-x[/tex]
Multiply by -1 both sides
[tex]-6> x[/tex]
Rewrite
[tex]x < -6[/tex]
The solution is the interval ----> (-∞, -6)
All real numbers less than -6
In a number line, the shaded area at left of x=-6 (open circle)
What is the solution of sqrt x+2-15=-3
Answer:
Step-by-step explanation:
Without brackets, we are not exactly sure what is under the root sign. There are 3 choices.
sqrt(x) + 2 - 15 = - 3
sqrt(x + 2) - 15 = - 3
sqrt(x + 2 - 15) = - 3
I think the middle one is what you intend. If not leave a note.
sqrt(x + 2) - 15 = - 3 Add 15 to both sides.
sqrt(x + 2) - 15+15 = - 3+15 Combine
sqrt(x + 2) = 12 Square both sides
x + 2 = 12^2 Do the right
x + 2 = 144 Subtract 2 from both sides.
x + 2-2 = 144-2
x = 142
Answer:
142
Step-by-step explanation:
What is the range of this promblem
Answer:
3
Step-by-step explanation:
Range is the largest number minus the smallest number
4-1 = 3
The range is 3
Answer:
3
Step-by-step explanation:
The range of a set of data is the difference between the highest and lowest values in the set.
Sort your data from lowest to highest. You get
1, 2, 3, 4, 4, 4, 4, 4
Highest value = 4
Lowest value = 1
Range = 3 chocolate chips
Which description of the graph of the linear equality y > 3x - 8 is correct?
The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded below
the line
The graph will be a solid line with a y-intercept of three and a slope of negative eight. The graph will be shaded above the
line
The graph will be a solid line with a y-intercept of three and a slope of negative eight. The graph will be shaded below the
line
The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above
the line
Answer:
Option The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above
the line
Step-by-step explanation:
we have
[tex]y>3x-8[/tex]
The solution of the inequality is the shaded area above the dashed line The equation of the dashed line is [tex]y=3x-8[/tex]
The slope of the dashed line is positive [tex]m=3[/tex]
The y-intercept of the dashed line is -8
see the attached figure to better understand the problem
Answer:
D is the correct answer
Step-by-step explanation:
Express 0.0000594 using scientific notation
Answer:
5.94×10^6
Step-by-step explanation:
you have to move the decimal 6 times before reaching the next number then you have to mutiply it by 10 and put the 6
Evaluate |-7| + 3|4|
A. 0
B.5
C.19
The answer is going to be 19.
Answer:
C. 19
Step-by-step explanation:
Order of operationsPEMDAS
Parenthesis
Exponent
Multiply
Divide
Add
Subtract
[tex]|-7|=7[/tex]
[tex]3|4|=3*4=12[/tex]
Add.
[tex]7+12=19[/tex]
[tex]19[/tex], is the correct answer.
write an inequality for the sentence: twice a number, decreased by the quotient of that number and 2, is at least 2
Answer:
2x - (x/2) >12
Step-by-step explanation:
Please mark brainliest and have a great day!
Use the function f(x) = 15 - x to answer the question.
Evaluate. (f · f)(2)
A) 0
B) 2
C) 4
D) 13
Answer:
B
Step-by-step explanation:
To evaluate (f ￮ f)(2) substitute x = 2 into f(x) and evaluate. Then substitute this value into f(x)
f(2) = 15 - 2 = 13, then
f(13) = 15 - 13 = 2
Hence (f ￮ f)(2) = 2
Solve for x -1/6x=7
Answer:
x= 42/5
alternative forms:
x=8 2/5
x=8.4
Step-by-step explanation:
Start with x-1/6x=7
Multiply both sides by 6 to get 6x-x=42
combine like terms (the Xs) to get 5x (6x-x is 5x)
5x=42
divide both sides by 5 to get x=42/5
Answer:
x = 42/5
Step-by-step explanation:
x -1/6x=7
Get a common denominator
6/6x - 1/6 x = 7
5/6x = 7
Multiply each side by 6/5 to isolate x
6/5 * 5/6x = 6/5*7
x = 42/5
Emily is a geometry teacher. She asks each student to bring in a cutout of a parallelogram. She tells them that one angle must measure 50° and the length of one side must be 10 centimeters. Emily also states that the parallelogram must not be a rhombus, rectangle, or square. Using this information, each student can prepare (________) parallelogram(s).
A- 0
B- 1
C- 2
D- Infinitely many
Answer:
D
Step-by-step explanation:
There are infinitely many possible parallelograms. The angles are fixed at 50° and 130°, and two parallel sides are fixed at 10 cm, but the other two sides can have any length (except 10 cm).
Which symbol correctly compares these fractions?
9 36
10 40
Answer:
=
Step-by-step explanation:
9/10 vs 36/40
Multiply 9/10 by 4/4 so the denominators are equal
9/10*4/4 = 36/40
36/40 vs 36/40
They are equal
write 5 in the form of a/b using integers to show it as a rational number
Answer:
a = 5, b=1
Step-by-step explanation:
We can rewrite a whole number as a fraction by putting it over 1
5/1 = 5
a = 5, b=1
5/1 is a rational number since it can be written in the form a/b
What is the pattern in the values as the exponents increase?
Answer:
Option D is correct.
Step-by-step explanation:
The first value is 1/32
if we multiply 1/32 with 2 i.e 1/32*2 we get 1/16
So, next value is 1/16
if we multiply 1/16 with 2 i.e 1/16 * 2 we get 1/8
So, next value is 1/8
if we multiply 1/8 with 2 i.e 1/8 * 2 we get 1/4
So, next value is 1/4
if we multiply 1/4 with 2 i.e. 1/4 *2 we get 1/2
so, next value is 1/2
if we multiply 1/2 with 2 i.e 1/2 * 2 we get 1
So, Option D multiply the previous value by 2 is correct.
What is the best approximation of a 15% tip on a $38 car wash?
Answer:
15% of 38= 5.7
Round up to 6
Answer: b) $6
Step-by-step explanation:
Please mark brainliest and have a great day!
the volume of a cylinder is 540 pi ft^3 the height is 15 ft. what is the diameter
a. 6
b.12
c.24
d.36
Answer:
12
Step-by-step explanation:
Volume of cylinder is pi*r^2*h (this is equal to 540pi in this case)
So we have 540pi=pi*r^2*h
this means that 540=r^2*h (I just divided both sides by pi since both sides were being multiplied by pi)
The height,h, is 15 so plug in 540=r^2*15
Divide both sides by 15 giving 540/15=r^2
So r^2=36
So r=6
The diameter,d, is twice the radius, r.
So d=2(6)=12
Answer:
b. 12
Step-by-step explanation:
The volume of a cylinder is
[tex]\pi {r}^{2} h[/tex]
Let us compose an equality and solve for the radius.
540pi = pi × r^2 × 15.
Divide both sides of the equation by 15pi.
r^2 = 36
r = +/- 6.
Length cannot be negative, so r = 6.
diameter = 2 × r. In this case,
d = 2 × 6 = 12.
The diameter is 12 ft.
The solutions to the inequality y s 2x - 4 are shaded on the
graph. Which point is a solution?
O (-1, 1)
O (1,-1)
O (3, 2)
O (2, 3)
5432
Answer:
C. (3, 2)
Step-by-step explanation:
(3, 2) is the solutions to the inequality y ≤ 2x − 4 shaded region.
If my fraction is 10/60 whats my decimal
Answer:
10/60 as a decimal is:
0.166666667
Step-by-step explanation:
To get 10/60 converted to decimal, you simply divide 10 by 60.
Please mark brainliest and have a great day!
Answer:
0.166666666666667
Step-by-step explanation:
evaluate the following expression: 2(1,1) -4(0,1). enter your answer as a vector.
Answer:
The answer is (2,-2)
You just distribute the 2 into (1,1) and same with the -4 into (0,1) and add them together
Step-by-step explanation:
ANSWER
[tex]\binom{2 }{ - 2}[/tex]
EXPLANATION
We were given the vector equation:
[tex]2 \binom{1}{1} ) - 4 \binom{0}{1} [/tex]
We perform the scalar multiplications first to get:
[tex]\binom{2 \times 1}{2 \times 1} ) - \binom{4 \times 0}{4 \times 1}[/tex]
Simplify the components of each vector
[tex]\binom{2 }{2} - \binom{0}{4}[/tex]
We subtract the corresponding components of the vector to get:
[tex]\binom{2 - 0}{2 - 4} [/tex]
This simplifies to
[tex]\binom{2 }{ - 2}[/tex]
6/y=9/24 whats the proportion?
a= 16
b= 19
c= 20
d=21
Answer:
a = 16
First exclude any restricted values of y.
6/y = 9/24 , y is not equal 0
Simplify the right side of the equation using 3.
6y = 3/8
Cross multiply.
6 x 8 = 3
3 x y = 3y
6 x 8 = 3y
48 = 3y
Switch the sides of the equation.
3y = 48
Divide both sides by 3.
3y/3 = y
48/3 = 16
Given: x + y = 6.
If XE (-15, -6, -1), then which of the following sets of ordered pairs are solutions?
© {(-15, -21), (-6, -12), (-1, -7)}
[(-15, 21), (-6, 12).(-1, 7)}
{(-15, 21), (-6, 12), (-1, -7)}
Answer:
[(-15, 21), (-6, 12).(-1, 7)}
Step-by-step explanation:
we have
x+y=6
Find the values of y for XE (-15, -6, -1)
so
For x=-15
-15+y=6 --->y=21
therefore
a solution is the point (-15,21)
For x=-6
-6+y=6 --->y=12
therefore
a solution is the point (-6,12)
For x=-1
-1+y=6 --->y=7
therefore
a solution is the point (-1,7)
The set of ordered pairs that are solutions is
[(-15, 21), (-6, 12).(-1, 7)}
Final answer:
The correct set of ordered pairs, which are the solutions to the equation x + y = 6 given x in {-15, -6, -1}, is {(-15, 21), (-6, 12), (-1, 7)}.
Explanation:
To determine which set of ordered pairs are solutions to the given equation x + y = 6, we need to plug the x-values into the equation and solve for y.
For x = -15: -15 + y = 6. Solve for y: y = 6 + 15 = 21. So the pair is (-15, 21).For x = -6: -6 + y = 6. Solve for y: y = 6 + 6 = 12. So the pair is (-6, 12).For x = -1: -1 + y = 6. Solve for y: y = 6 + 1 = 7. So the pair is (-1, 7).The correct set of ordered pairs is therefore {(-15, 21), (-6, 12), (-1, 7)}.
What is answer to the equation 81x=x^2 ?
For this case we have the following equation:
[tex]81x = x ^ 2[/tex]
Rewriting we have:
[tex]x ^ 2-81x = 0[/tex]
We take common factor "x" from both terms:
[tex]x (x-81) = 0[/tex]
It is observed that equality is fulfilled when x = 0 and when x = 81
So, the roots are:
[tex]x_ {1} = 0\\x_ {2} = 81[/tex]
Answer:
[tex]x_ {1} = 0\\x_ {2} = 81[/tex]
Can someone please help me With BOTH parts of the question ..thanks u
Answer:
-0.89 < -0.51
B. Felipe's Restaurant has less value than Ming's Lodge.
Step-by-step explanation:
If you have a big debt you're going to have less money.
The two solids are similar, and the ratio between the lengths of their edges is
2.7. What is the ratio of their surface areas?
A. 4:14
B. 4:49
C. 2:7
D. 8:343
Please explain how to do if not too lazy to do so (: thanks!
Answer:
The ratio of their surface areas is 4:49
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor
In this problem the scale factor is equal to the ratio 2:7
and
Remember that
If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared
therefore
In this problem the ratio of their surface areas is (2:7)^2 = 4:49
The ratio of their surface areas is,
⇒ 4 : 49
What is mean by Ratio?A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.
Where, x and y are individual amount of two quantities.
And, Total quantity gives after combine as x + y.
\
We know that;
If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor.
In this problem the scale factor is equal to the ratio 2/7,
Hence, If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared
therefore,
In this problem the ratio of their surface areas is ,
⇒ (2 / 7)²
⇒ 4 / 49
⇒ 4 : 49
Thus, The ratio of their surface areas is,
⇒ 4 : 49
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An investment will pay $100 at the end of each of the next 3 years, $200 at the end of Year 4, $300 at the end of Year 5, and $500 at the end of Year 6. If other investments of equal risk earn 8% annually, what is its present value? Its future value?
Answer:
$1,466.23 Will be your answer mate !!!!!!
Step-by-step explanation:
The present value is calculated by discounting each of the cash flows to the present therefore if we assume no salvage value:
PV = $100 / 1.08 + $100 / 1.08^2 + $100 / 1.08^3 + $200 / 1.08^4 + $300 / 1.08^5 + $600 / 1.08^6
PV = $923.98
Technically, as we have assumed there are no salvage value then in the future value will be zero. If you are asking how much remains in the investment. If you are asking how much the investment has yielded, keep in mind that the cash flows are not by definition reinvested so the time value of those cash flows can't be accounted for. If you do not account for the time value of those cash flows then the future value is just:
$100 * 3 + $200 + $300 + $500 = $1,300
However if you use the 8% per annum effective rate as a discount rate to take into consideration the time value of the money which is basically saying that you can reinvest the cash flows at 8% per annum effective then the future value would be:
$100 * 1.08^5 + $100 * 1.08^4 + $100 * 1.08^3 + $200 * 1.08^2 + $300 * 1.08 + 500 = $1,466.23
you'll get your answer as : $1,466.23 !
Final answer:
The present value of the investment with varying cash flows and an 8% discount rate is $943.28. The future value, assuming reinvestment at an 8% interest rate until the end of Year 6, is $1,466.23.
Explanation:
To calculate the present value of the investment with varying cash flows and an 8% discount rate (interest rate), we discount each cash flow to its present value using the formula [tex]PV = FV / (1 + r)^t,[/tex]where PV is present value, FV is future value, r is the annual interest rate, and t is the number of years until the payment.
Year 1: [tex]\$100 / (1 + 0.08)^1 = $92.59[/tex]
[tex]Year 2: \$100 / (1 + 0.08)^2 = $85.73 \\Year 3: \$100 / (1 + 0.08)^3 = $79.38 \\Year 4: \$200 / (1 + 0.08)^4 = $150.26 \\Year 5: \$300 / (1 + 0.08)^5 = $220.08 \\Year 6: \$500 / (1 + 0.08)^6 = $315.24 \\[/tex]
The sum of these values is the total present value of the investment, which equals $943.28.
For the future value, we grow each cash flow by the interest rate for the remaining period it would be invested until the end of Year 6, since payments are made at the end of each year.
[tex]Year 1: \$100 * (1 + 0.08)^5 = $146.93 \\Year 2: \$100 * (1 + 0.08)^4 = $136.05 \\Year 3: \$100 * (1 + 0.08)^3 = $125.97 \\Year 4: \$200 * (1 + 0.08)^2 = $233.28 \\Year 5: \$300 * (1 + 0.08)^1 = $324.00 \\[/tex]
Year 6: $500 = $500.00
By adding all future values, the total future value of the investment is $1,466.23.
What do I do?????❓‼️❓‼️❓‼️❓‼️
Working and answer in the photo above. Hope this helps
Given 4 coordinate points A(2,0), B(4,0), C(5,-2), D(1, -2), click in the figure until the image that is rotated by 180° about
the origin O appears.
The origin O appears rotated by 180° about ’( -2,0), (-4,0), (-5,2) , ’(-1,2).
What is coordinate geometry?Coordinate geometry (or analytic geometry) is described as the examination of geometry and the use of coordinate factors. using coordinate geometry.
Coordinate using the horizontal and vertical distances from the two reference axes. generally represented by way of (x,y) the x-price and y-cost.
Coordinate geometry is used to control and regulate air visitors. The coordinates of the flight are used to describe the plane's modern location. despite the fact that a plane actions a tiny distance (up, down, forward, or backward), the machine updates the coordinates of flight for each small change in its role.
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