Find when f(x) = 0. By factorizing, we have
-x² + 8x - 7 = - (x - 7) (x - 1) = 0
so either x - 7 = 0 or x - 1 = 0, or simply x = 1 or x = 7.
Split the domain into three intervals, and check the sign of f(x) over each interval at some test point in the interval. The sign will tell you when the icicle is dripping (positive) or not (negative).
• [0, 1) : at x = 0, we have f(0) = -7 < 0
• (1, 7) : at x = 2, we have f(2) = 5 > 0
• (7, 10] : at x = 8, we have f(8) = -7 < 0
This tells us that the icicle is not dripping when 0 ≤ x < 1, begins to drip when x = 1, drips for the duration of 1 < x < 7, stops dripping when x = 7, and keeps on not dripping when 7 < x ≤ 10.
Arianna invests $5600 in a new savings account which earns 5.4% annual interest, compounded quarterly. What will be the value of her investment after 8 years? Round to the nearest cent.
The value of her investment after 8 years is $8,293.81.
What do interest rates mean?
An interest rate tells you how high the cost of borrowing is, or high the rewards are for saving.
Given:
P= $5600
r= 5.4%
t= 8 years
Then solve the equation for A
A = P(1 + r/n)^nt
A = 5,400.00[tex](1 + 0.054/4)^{4/8}[/tex]
A = 5,400.00[tex](1 + 0.0135)^{32}[/tex]
A = $8,293.81
Hence, the value will be $8,293.81.
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If a cylinder has a volume of 120 cm3 and a cone has a volume of 360 cm3, is it possible that the two cones have congruent bases and congruent heights?
No, the cone and the cylinder can't have congruent heights and bases.
is it possible that the two cones have congruent bases and congruent heights?
The volume of a cylinder of radius R and height H is:
V = pi*R^2*H
And for a cone of radius R and height H is:
V = pi*R^2*H/3
So, for the same dimensions R and H, the cone has 1/3 of the volume of the cylinder.
Here, the cylinder has a volume of 120cm³ and the cone a volume of 360cm³, so the cone has 3 times the volume of the cylinder.
This means that the measures must be different, so the cone and the cylinder can't have congruent heights and bases.
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Represent "The product of 9 and a number y" mathematically.
Answer:
9y
Step-by-step explanation:
Mathematicaly, the product of 9 and a number "y" is:
9y
Given the function h of x equals 8 times the cube root of x minus 6 end root plus 16, what is the x-intercept of the function?
–6
–2
2
16
The x-intercept of the function [tex]h(x) = 8 * \sqrt[3]{x - 6} + 16[/tex] is -2
How to determine the x-intercept?The equation of the function is given as:
[tex]h(x) = 8 * \sqrt[3]{x - 6} + 16[/tex]
The x intercept is the x value when h(x) = 0
So, we have:
[tex]8 * \sqrt[3]{x - 6} + 16 = 0[/tex]
Subtract 16 from both sides
[tex]8 * \sqrt[3]{x - 6} = -16[/tex]
Divide both sides by 8
[tex]\sqrt[3]{x - 6} = -2[/tex]
Take the cube of both sides
x - 6 = -8
Add 6 to both sides
x = -2
Hence, the x-intercept of the function [tex]h(x) = 8 * \sqrt[3]{x - 6} + 16[/tex] is -2
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=
An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded contir
equation 200e0.08 - 350 represents the situation, where t is the number of years the money has been i
how long has the money been invested? Use a calculator and round your answer to the nearest whole
O 5 years
O 7 years
O 19 years
O 22 years
Answer:
7 years
Step-by-step explanation:
Your equation should read = 200 * e^(.08 t) = 350
solving for t = 6.99 yrs ~~ 7 years
Item 11 In the table, Pattern A uses the rule "add 5" and Pattern B uses the rule "add 10." Pattern A 10 15 20 25 30 Pattern B 20 30 40 50 60 Which statement is true? Every term in Pattern B is 12 the corresponding term in Pattern A. Every term in Pattern B is 10 times the corresponding term in Pattern A. Every term in Pattern B is 2 times the corresponding term in Pattern A. Every term in Pattern B is 10 more than the corresponding term in Pattern A. PLESAAAA HELP I NEED TO PASS 5 GRADE IF I FAIL I WONT PASS PLSSSSSSSSSSSSSS tysm!
The Pattern B is the twice of the Pattern A. Then the correct option is C.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Item 11 In the table,
Pattern A uses the rule "add 5" and Pattern B uses the rule "add 10".
Pattern A 10 15 20 25 30
Pattern B 20 30 40 50 60
Then the Pattern B is the twice of the Pattern A.
Then the correct option is C.
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If events A and B are independent, and the probability that event A occurs is 83%, what must be true?
The probability that event B occurs is 17%.
The probability that event B occurs is 83%.
The probability that event A occurs, given that event B occurs, is 83%.
The probability that event B occurs, given that event A occurs, is 83%.
Answer:
c
Step-by-step explanation:
edge 2023
The probability that event B occurs is 83%. Therefore, option C is the correct answer.
What is the independent variable?Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or demand that they depend, by some law or rule, on the values of other variables.
Given that, events A and B are independent, and the probability that event A occurs is 83%.
If the outcome of one event has no bearing on the fate of the other, the two events are said to be independent events. Instead, we may say that an event is considered independent if it does not affect the likelihood of another event.
Since, the events A and B are independent, if the probability that event A occurs is 83%.
Then, the probability that event B occurs is 83%.
Therefore, option C is the correct answer.
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Check whether the following differential equation is exact or not. If not, then convert it into an exact differential equation.
[tex]2ydx+(x-sin\ y^{\frac{1}{2} } )dy =0[/tex]
The given differential equation is not exact, if we convert it to an exact one, we get:
[tex]2ydx + 2*(x - sin(y)^{1/2})*dy = 0[/tex]
Is the differential equation exact or not?A differential equation:
[tex]Ndx + Mdy = C[/tex]
Is exact only if:
[tex]\frac{dM}{dy} = \frac{dN}{dx}[/tex]
In this case, we have:
[tex]2ydx + (x - sin(y)^{1/2})*dy = 0\\\\then:\\\\N = 2y\\M = x - sin(y)^{1/2}[/tex]
If we differentiate, we will get:
[tex]\frac{dN}{dy} = 2\\\\\frac{dM}{dx} = 1[/tex]
So, to convert this to an exact differential equation, we need to add a factor 2 to N, this will give:
[tex]2ydx + 2*(x - sin(y)^{1/2})*dy = 0[/tex]
This is, in fact, an exact differential equation.
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Help please!
Select the correct answer.
A fan in a baseball stadium is sitting in a seat with their eye level is a vertical distance of 350 ft above level.
A) When the fan is looking at home plate, the angle of depression is 30°. What is the horizontal distance from the fan to home plate? Round to the nearest 10th. Explain two different ways to determine this distance.
B) The same fan makes eye contact with a second fan in the stands that is seated at a lower row in the stadium. The straight-line distance between the eyes of the two fans is 300 ft and the angle of depression is 48°. What is the vertical distance between field level and the eyes of the second fan? Round to the nearest tenth.
A store is having a 20% off sale.The sale price of an item with price p is p-0.2p.what is an equivalent expression
Answer:
0.8p
Step-by-step explanation:
Hello!
As the questions states, 20% of p is 0.2p.
Simplifying the equation:
p - 0.2p0.8p0.8p is also 80% of p, which can be translated to 100% - 20% of p.
The equivalent expression is 0.8p.
What is the product?
(-2x-9y²)(-4x-3)
Answer:
8x^2 +6x +36xy^2+27y^2
Step-by-step explanation:
2x * 4x-2x*-3) -9y-^2(-4x)-9y^2(-3)
Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
3^5
Step-by-step explanation:
exponents:
1 - ( - 4 ) = 5
Therefore,
3^5
Write the numbers in each circle that is described by the attribute written outside the circle. Numbers in the overlapping regions must meet the requirements of each circle. Justify why you placed the numbers in the overlapping regions.
The attached image represents the completed Venn diagrams
How to complete the circles?Diagram 1
We have:
Multiples of 3 and Multiples of 10
When the sets are populated, we have:
Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
Multiples of 10 = 10, 20, 30
Both = 30
Next, we complete the circles using the above data values
See attachment 1
Diagram 2
We have:
Multiples of 2, Multiples of 3 and Multiples of 5
When the sets are populated, we have:
Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30
Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
Multiples of 5 = 5, 10, 15, 20, 25, 30
Multiples of 2 and 3 = 6, 12, 18, 24 and 30
Multiples of 2 and 5 = 10, 20 and 30
Multiples of 3 and 5 = 15 and 30
All = 30
Next, we complete the circles using the above data values
See attachment 2
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Compute the NPV for Project M if the appropriate cost of capital is 9 percent. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your final answer to 2 decimal places.) Project M Time: 0 1 2 3 4 5 Cash flow: −$2,400 $630 $760 $800 $880 $380 Should the project be accepted or rejected? multiple choice accepted rejected
The net present value is $305.73. The project should be accepted.
Net present valueUsing this formula
Net present value=Cashflow÷(1+Cost of capital)^ time
Let plug in the formula
Net present value=-$2,400+ ($630÷(1+.09)^1) + ($760÷(1+.09)^2) + ($800÷(1+.09)^3) + ($880 ÷(1+.09)^4) + ($380÷(1+.09)^5)
Net present value=-$2,400+ ( $630÷(1.09)^1) + ($760÷(1.09)^2) + ($800÷(1.09)^3) + ($880 ÷(1.09)^4) + ($380÷(1.09)^5)
Net present value=-$2,400+ ($630÷1.09) + ($760÷1.1881) + ($800÷1.295029) + ($880 ÷1.41158161) + ($380÷1.538639549)
Net present value=-$2,400+ $577.98+$639.68+$617.75+623.41+$246.91
Net present value=$305.73
Based on the above calculation the project should be accepted.
Therefore the NPV is $305.73.
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Tell whether the angles are adjacent or vertical. Then find the value of x.
Answer:
These are Vertical angles, adjacent angles are next to each other and make up a whole angle, while vertical angles are across and equal the same thing.
X = 81 because 84 and (x + 3) are the same so 84 minus 3 is 81
Hope that helps
Pls help with my math work
An insurance data scientist is researching a certain stretch of a rural highway where drivers are never pulled over. The mile markers in the solution of the following inequality determines the conclusion of his research. Solve and interpret the compound inequality, where x represents the mile marker along the highway.
Answer:
Drivers located below mile marker 47 or at mile marker 70 or above never get pulled over.
Step-by-step explanation:
enter the ordered pair that is the solution to the system of equations graphed below. y= -4x+2 y=x-3
Answer:
Step-by-step explanation:
-4x + 2 = x - 3
-5x + 2 = -3
-5x = -5
x = 1
y = 1 - 3
y = -2
(1, -2)
Which statements are true about the dollhouses? Select three options.
The space inside dollhouse 1 can be found using the equation V = 6 (6) (5) + one-half (6) (6) (4).
The space inside dollhouse 1 can be found using the equation V = 6 (6) (5) + one-third (6) (6) (4).
The space inside dollhouse 2 can be found using the equation V = 6 (6) (5) + one-half (6) (6) (4).
The space inside dollhouse 2 can be found using the equation V = 6 (6) (5) + one-third (6) (6) (4).
The space inside dollhouse 1 is 24 inches cubed greater than the space inside dollhouse 2.
The statements that are true about the dollhouses is: 1,4,5.
True statement about dollhouseThe space inside dollhouse 1 can be found using the equation V = 6 (6) (5) + one-half (6) (6) (4).
Space inside dollhouse 1:
V = 6 (6) (5) + 1/2 (6) (6) (4)
V=180+72
V=252 inches
The space inside dollhouse 2 can be found using the equation
V = 6 (6) (5) + 1/3 (6) (6) (4)
V=180+48
V=228
The space inside dollhouse 1 is 24 inches cubed greater than the space inside dollhouse 2.
V1=252
V2=228
Hence:
252-228=24 inches cubed
V1 ≥V2
Therefore the statements that are true about the dollhouses is: 1,4,5.
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What is the maximum probability of committing a Type I error that the researcher is willing to commit? a. Critical values b. p-value c. Level of Significance d. Confidence level
Answer: c. Level of Significance
This is the alpha value
alpha is a greek letter with the symbol [tex]\alpha[/tex]
A type 1 error is when the researcher rejects the null, but the null was true (meaning the researcher shouldn't have rejected the null).
Please help quickly!!
The values of a, b and c from the given exponential function are 7, 9 and 4 respectively
Laws of indicesAccording to the exponential law of indices
[tex]\sqrt[c]{a^b}[/tex]
This can be written as;
[tex]\sqrt[c]{a^b}=a^{\frac{b}{c} }[/tex]
Given the exponential expression
[tex]7^\frac{9}{4}[/tex]
Compare with the original expression
a = 7, b = 9 and c = 4
Hence the values of a, b and c from the given exponential function are 7, 9 and 4 respectively
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Simplify the expression
(2x^2y)3
Answer: Heyaa! ~
When simplifying (2x^2y)3 the answer will be... 6x²y
Step-by-step explanation:
Multiply the numbers:
2x²y · 3 6x²yHopefully this helps you! ^^
I need help finding the values of the last boxes shown in the image.
The region R is bounded by the x-axis, the straight line in the graph and the vertical line x+2.
The volume of the region R bounded by the x-axis is: [tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}[/tex]
What is the volume of the solid revolution on the X-axis?The volume of a solid is the degree of space occupied by a solid object. If the axis of revolution is the planar region's border and the cross-sections are parallel to the line of revolution, we may use the polar coordinate approach to calculate the volume of the solid.
In the graph, the given straight line passes through two points (0,0) and (2,8).
Therefore, the equation of the straight line becomes:
[tex]\mathbf{y-y_1 = \dfrac{y_2-y_1}{x_2-x_1}(x-x_1)}[/tex]
where:
(x₁, y₁) and (x₂, y₂) are two points on the straight lineThus, from the graph let assign (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 8), we have:
[tex]\mathbf{y-0 = \dfrac{8-0}{2-0}(x-0)}[/tex]
y = 4x
Now, our region bounded by the three lines are:
y = 0 x = 2y = 4xSimilarly, the change in polar coordinates is:
x = rcosθ, y = rsinθwhere;
x² + y² = r² and dA = rdrdθNow
rsinθ = 0 i.e. r = 0 or θ = 0rcosθ = 2 i.e. r = 2/cosθrsinθ = 4(rcosθ) ⇒ tan θ = 4; θ = tan⁻¹ (4)⇒ r = 0 to r = 2/cosθ θ = 0 to θ = tan⁻¹ (4)Then:
[tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^2 (rdr d\theta )}[/tex]
[tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}[/tex]
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SO CONFUSED PLEASE SOMEONE EXPLAIN! DUE SOON AND NEED HELP!!!!!!!! QUESTION IN PICTURE BELOW
Answer:
=> Apply law of cosine
[tex]c^2=a^2+b^2-2abcos\left(C\right)[/tex]
=> input value
[tex]z^2=6.5^2 + 9.4^2-\left(6.5\right)\left(9.4\right)\left(cos\left(131\right)\right)[/tex]
=> simplify
[tex]z=\sqrt{\left(6.5^2+\:9.4^2\right)-\left(6.5\right)\left(9.4\right)\left(-0.65605902899\right)}[/tex]
=> calulcation
[tex]z=\sqrt{-61.1\cos \left(131^{\circ \:}\right)+130.61},\:z=-\sqrt{-61.1\cos \left(131^{\circ \:}\right)+130.61}[/tex]
=> apply rule: Distance must be greater than 0
which is about 14.51828
What is the value of x? Enter your answer in the box.
Answer:
x = 25
Step-by-step explanation:
the line QC is parallel to BR
Then
x/15 = 40/24
Then
24x = 40×15
Then
24x = 600
Then
x = 600/24
Then
x = 25
Find the inverse
[tex]f(x)={e}^{3x - 1} [/tex]
Tank you for your support
Answer:
[tex]f^{-1}(x)=\dfrac{1}{3}(\ln x +1)[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=e^{3x-1}[/tex]
Replace f(x) with y:
[tex]\implies y=e^{3x-1}[/tex]
Take natural logs of both sides:
[tex]\implies \ln y = \ln e^{3x-1}[/tex]
Apply the Power Log Law [tex]\ln x^n=n\ln x[/tex] :
[tex]\implies \ln y = (3x-1)\ln e[/tex]
As [tex]\ln e=1[/tex] then:
[tex]\implies \ln y = 3x-1[/tex]
Rearrange to make x the subject:
[tex]\implies 3x=\ln y +1[/tex]
[tex]\implies x=\dfrac{1}{3}(\ln y +1)[/tex]
Swap x for [tex]f^{-1}(x)[/tex] and y for x:
[tex]\implies f^{-1}(x)=\dfrac{1}{3}(\ln x +1)[/tex]
please help me with thiss
Answer:
the fourth option is correct
Step-by-step explanation:
the first equation represents that the cost of 6 bananas is the same as the cost of nine apples. therefore, y is the cost of a single banana and x is the cost of a single apple. the second equation represents the situation of you buying 4 bananas and 2 apples for $8. If x and y represent the cost of each fruit, then the point (x,y) = (1,1.5) means that x, the cost of an apple, is $1.00 and that y, the cost of a banana, is $1.50.
What the answer to this question please
[tex]V=lwh=(3)\left(\frac{4}{3} \right) \left(\frac{3}{5} \right)\\\\V=3\left(\frac{12}{15} \right)\\\\V=\frac{36}{15}=\boxed{\frac{12}{5} \text{ cm}^{2}}[/tex]
Convert 2 1/8 into an improper fraction.
Answer:
17/8
Step-by-step explanation:
You must type 2* 8 and add 1. That makes 17/8
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to convert 2 1/8 into an improper fraction (a fraction whose numerator is greater than its denominator).
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Follow three easy steps! ^-^These are the steps:
Multiply the whole part (2) times the denominator (8). This gives us 16.Now, add the numerator, 1: 17. This is the numerator of the new fraction.Simplify if possible.However, we cannot simplify 17/8, so that's our answer.
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