The required f(x) is positive on the intervals (-2,1) and (1.1547,3).
What is Function?A function in mathematics from a set X to a set Y assigns precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two variable quantities.
According to question:To determine the intervals on which the function is positive on the interval (-3,3), we need to find the x-values for which f(x) is greater than zero (i.e., positive).
First, we can find the critical points of the function by finding where f(x) = 0:
[tex]$\begin{align*}f(x) &= 2x^3 -7x +4 \0 &= 2x^3 -7x +4 \&= (x-1)(2x^2+2x-4) \&= (x-1)(2(x-1)(x+2)) \\end{align*}[/tex]
So the critical points are x = 1 and x = -2.
Next, we can test the sign of f(x) on different intervals. Since f(x) is a polynomial function and is continuous on the interval (-3,3), we only need to test the sign of f(x) at the critical points and at the endpoints of the interval:
f(-3) &= 2(-3)³ -7(-3) +4 = -47 <0
f(-2) &= 2(-2)³ -7(-2) +4 = 0
f(1) &= 2(1)³ -7(1) +4 = -1 < 0
f(3) &= 2(3)³ -7(3) +4 = 47 > 0
Therefore, f(x) is positive on the intervals (-2,1) and (1.1547,3), where the boundaries of the intervals are rounded to four decimals. Therefore, the answer is:
[tex]$$\boxed{(-2,1) \text{ and } (1.1547,3)}$$[/tex]
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Please Help Me I Got 1 Hour To Do It...
Brainlyiest To The 1st Answer!
After answering the provided question, The pyramid's surface area is 64 inch²
Prism is what?An n-sided quadrilateral prism is a polyhedron with n sides, an n-sided quadrilateral base, a second base that is a copy of the first base moved, and n extra heads (necessarily all parallelograms), often two of which connect the corresponding sides of the base.
Translations are all cross sections that appear to be parallel to the base. A prism is a multifaceted, solid, three-dimensional object. Its horizontal flanks, bases, and cross sections are all the same. The faces of a prism are parallelograms or bases-free quadrilaterals. A prism is a clear, solid, homogenous refracting device that is surrounded by planes that are just slightly inclined to one another. Two triangular heads and two parallel rectangular faces are the typical features of a prism.
here in the give figure we have a pyramid,
The pyramid's surface area is given as,
[tex]A = 4(Area $ of $ triangle) + Base $ area$[/tex]
[tex]A = 4*(1/2*6*4) + 4 * 4 \\A = 4 \times (34) + 16 \\A = 4 \times 12 +16A = 48 +16\\A = 64[/tex]
Therefore, The pyramid's surface area is 64 inch²
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Use the gcf to factor the expression 40x+24y-56
Answer:
40x+24y-56=
8(5x+2y-7)
Step-by-step explanation:
Heather invests $4,625 in an account with a 3.5% interest rate, making no other deposits or withdrawals. What will Heather’s account balance be after 5 years if the interest is compounded 2 times each year?
Heather’s account balance be after 5 years if the interest is compounded 2 times each year is $[tex]4,625*(1.0175)^{10}[/tex].
The amount of money you have available in your checking or savings account is known as your account balance in the world of banking. The net amount remaining in your account after all deposits and credits have been balanced against any charges and debits is your account balance.
We know that
A= [tex]P(1+m/n)^{n}[/tex]
A=[tex]P(1+3.5/280)^{10}[/tex]
A= [tex]4625*(1.0175)^{10}[/tex]
Amount= $[tex]4,625*(1.0175)^{10}[/tex]
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can someone help me pls
Data insufficient or not properly mentioned.
Define the term Circle?The points in a plane that are equally spaced apart from a fixed point known as the center make up a circle, which is a two-dimensional geometric object. The radius, represented by the letter "r," is the distance a circle's center is from any point on its surface. The diameter of a circle is the length of any line segment that connects any two locations on the circle and passes through its center. The diameter is two times longer than the radius.
The interior of the circle is the set of all points inside the circle, and the exterior of the circle is the set of all points outside the circle. When the diameter of a circle is multiplied by the mathematical constant pi (), the circumference, or distance around the circle, is obtained. C = 2r, where "C" stands for the circumference and "r" for the radius, is the formula for a circle's circumference.
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5 liters of olive oil is of rupees 912.50 pr 3 liters of 518.20 which option is better
Answer:
Step-by-step explanation: The 3 liters is the best option
Eva has a bag that contains pineapple chews, lemon chews, and watermelon chews. She performs an experiment. Eva randomly removes a chew from the bag, records the result, and returns the chew to the bag. Eva performs the experiment 19 times. The results are shown below: A pineapple chew was selected 7 times. A lemon chew was selected 6 times. A watermelon chew was selected 6 times. Based on these results, express the probability that the next chew Eva removes from the bag will be a flavor other than pineapple as a decimal to the nearest hundredth
Answer:
The total number of times Eva performed the experiment is 19. Out of these 19 times, a pineapple chew was selected 7 times, and a lemon chew and watermelon chew were selected 6 times each.
Therefore, the probability of selecting a flavor other than pineapple can be found by adding the number of times a lemon chew or watermelon chew was selected and dividing by the total number of times Eva performed the experiment:
P(selecting a flavor other than pineapple) = (number of times a lemon or watermelon chew was selected) / (total number of times the experiment was performed)
P(selecting a flavor other than pineapple) = (6 + 6) / 19
P(selecting a flavor other than pineapple) = 12 / 19
P(selecting a flavor other than pineapple) ≈ 0.63 (rounded to the nearest hundredth)
Therefore, the probability that the next chew Eva removes from the bag will be a flavor other than pineapple is approximately 0.63.
Step-by-step explanation:
Is 2x+y=5;(7,5) A solution?
After answering the presented question, we can conclude that Thus, equation (7, 5) is not a solution to the equation 2x + y = 5.
What is equation?An equation is a mathematical statement that validates the equivalent of two expressions joined by the equal symbol '='. For instance, 2x - 5 = 13. 2x-5 and 13 are two examples of expressions. The character '=' connects the two expressions. An equation is a mathematical formula that has two algebras on each side of an assignment operator (=). It demonstrates the equivalency link between the left and middle formulas. L.H.S. = R.H.S. (left side = right side) in any formula.
To see if the point (7, 5) is a solution to the equation 2x + y = 5, we can plug x = 7 and y = 5 into the equation and see if it holds true.
Hence, when we substitute x = 7 and y = 5 into 2x + y = 5, we get:
2(7) + 5 = 19
Because 19 is not equal to 5, the point does not satisfy the equation 2x + y = 5. (7, 5).
Thus, (7, 5) is not a solution to the equation 2x + y = 5.
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f(x) = 5x + 3
g(x) = 2x² -2x + 2
Find (fg(x))
Answer:
Step-by-step explanation:
Q1: For the functions f(x) = x + 2 and g(x) = 2x2-x find the following: ... Calculator in radians. = 2. T. 구. Score:
Brandon is saving up to buy a house. He is debt-free, has three months of expenses saved in his emergency fund, and is renting while he saves up enough money for the down payment for a mortgage. His take-home pay is $60,000.
What is Brandon’s monthly Take-home pay
By dividing the annual take-home pay, Brandon's monthly take-home pay is $5,000.
What is division?
Division is a basic arithmetic operation that involves splitting a number into equal parts or groups. It is the inverse operation of multiplication.
In division, we divide one number (the dividend) by another number (the divisor) to find out how many times the divisor goes into the dividend. The result of division is called the quotient.
To determine Brandon's monthly take-home pay, we need to divide his annual take-home pay by the number of months in a year.
Brandon's annual take-home pay is $60,000.
To find his monthly take-home pay, we divide this amount by 12 (the number of months in a year):
Monthly take-home pay = $60,000 / 12 = $5,000
Therefore, Brandon's monthly take-home pay is $5,000.
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please help asap it shouldent take too much time
What is x please I need help?
Answer:
x = 3
Step-by-step explanation:
Using alternate angles, these angles are congruent
20x + 9 = 27x - 12
27 - 20 = 7
12 + 9 = 21
21 / 7 = 3
x = 3
am cunfusd wat is 2+2
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
The Center for Disease Control and Prevention estimates the number of persons aged 13 and older living with HIV is 1.1 million. Assume the US population aged 13 and older is 300 million. The test for HIV has an accuracy rate of 97%. Use this information to complete a table of possibilities and answer the question below.
If someone tests positive for HIV, what is probability they don't actually have HIV?
(Express your answer rounded correctly to the nearest tenth of a percent!)
If someone tests positive for HIV, the probability they don't actually have HIV is 3%, due to the 97% accuracy rate of the test.
Table of Possibilities:
HIV Status No. of People Probability
Positive 1.1 million 3%
Negative 298.9 million 97%
If someone tests positive for HIV, the probability they don't actually have HIV is 3%. This is because the accuracy rate of the test is 97%, meaning that out of the 1.1 million people living with HIV, only 3% will receive a false-positive result. Additionally, a false-negative result can lead to delayed diagnosis and treatment, which can have serious health consequences. It is important to note that the accuracy of a test can vary depending on the type of test and the population being tested. Therefore, it is important to consult a healthcare provider to determine which test is right for you.
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What were two reasons why the Soviet Union faced critical economic issues during the late 1980s? mutipal answer
low numbers of educated workers
increased amount of defense spending
financial cost of war in Afghanistan failing economic infrastructures
no tax money from the Russian Orthodox Church
The two reasons why the Soviet Union faced critical economic issues during the late 1980s are:
Increased amount of defense spendingFailing economic infrastructureHow does the reasons affect the Soviet UnionIncreased amount of defense spending: The Soviet Union spent a significant portion of its resources on military and defense during the Cold War. By the 1980s, the arms race with the United States had intensified, and the Soviet Union continued to spend heavily on defense, putting a strain on the economy.
Failing economic infrastructure: The Soviet economy was plagued by inefficiencies, lack of innovation, and outdated technology. The centralized planning system, which had been the backbone of the Soviet economy, was unable to adapt to changing economic conditions. The economy was characterized by shortages of goods, low productivity, and poor quality of products. The lack of market mechanisms and private ownership hindered innovation and investment.
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What is the length of the the midsegment of a trapezoid with bases of length 16 and 26?
The length of the midsegment of the trapezoid is 21 units.
What is length of midsegment of the trapezoid?The midsegment of a trapezoid is a line segment that connects the midpoints of the two non-parallel sides of the trapezoid. It is parallel to the bases and its length is equal to the average of the lengths of the bases.
We are given that bases of the trapezoid have lengths of 16 and 26. To find the length of the midsegment, we need to find the average of these two lengths. The midsegment length is calculated as:
= (16 + 26) / 2
= 42 / 2
= 21 units.
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How many rational numbers are there between 0 and 5 explain your answer in words.
Answer:
There are Infinity rational numbers between 0 and 5.
Consider the graph of f(x) = 2/3(x-3)^2.
Select True or False for each statement about the graph.
A. The Vertex is (3,0). T/F
B. The minimum value is 0. T/F
C. The axis of symmetry is x = 2/3. T/F
I am learning about Graphing Quadratic Functions.
Step-by-step explanation:
A. true
the formula of a parabola is
y = a(x – h)2 + k.
(h, k) is the vertex.
so, yes, in (2/3)×(x - 3)² the vertex is (3, 0).
B. true
as per A.
and with positive "a" it opens up upwards.
C. false
the axis of symmetry is x = 3.
the line that goes through the vertex.
please help with this problem
The length of the sides of the similar triangles ΔRLM and ΔRST, indicates;
[tex]\overline{ST}[/tex] 16
What are similar triangles?Similar triangles are triangles for which two angles in one triangle are congruent in two angles in the other triangles, such that the triangles have the same shape but they have different sizes.
10. The possible details of the question, obtained from a similar online question are;
RL = 2, LS = 6, LM = 4, and ST = x + 2,
Required; The length of ST
The parallel lines, LM and ST, indicates that the angles;
∠RLM and ∠RST are congruent; ∠RLM ≅ ∠RST
∠RML and ∠RTS are congruent; ∠RML ≅ ∠RTS
Therefore; ΔRLM and ΔRST are similar
The ratio of the adjacent sides to congruent angles between similar triangles are equivalent, therefore;
[tex]\frac{RL}{LM} =\frac{RS}{ST}[/tex]
RS = RL + LS (Segment addition postulate)
Therefore; RS = 2 + 6 = 8
[tex]\frac{2}{4} =\frac{8}{x + 2}[/tex]
2 × (x + 2) = 4 × 8 = 32
2·x + 4 = 32
2·x = 32 - 4 = 28
x = 28/2 = 14
x = 14
ST = x + 2, therefore;
ST = 14 + 2 = 16
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find the area of the shaded polygons
The area οf the shaded pοlygοn is 15 square units.
What is Pοlygοn?A pοlygοn is 2-dimensiοnal clοsed shape with the straight sides. It is fοrmed by cοnnecting line segments called the sides. The sides οf pοlygοn meet at pοints called the vertices.
Tο find the area οf the shaded pοlygοns, we need tο first find the area οf the large rectangle and subtract the sum οf the areas οf the twο smaller rectangles.
The dimensiοns οf the large rectangle are 9 units by 7 units, sο its area is:
Area οf large rectangle = 9 x 7 = 63 square units
The dimensiοns οf the smaller rectangles are 3 units by 2 units and 2 units by 5 units, sο their areas are:
Area οf first small rectangle = 3 x 2 = 6 square units
Area οf secοnd small rectangle = 2 x 5 = 10 square units
Area οf shaded pοlygοn = Area οf large rectangle - (Area οf first small rectangle + Area οf secοnd small rectangle)
Area οf shaded pοlygοn = 63 - (6 + 10)
Area οf shaded pοlygοn = 47 square units
Therefοre, the area οf the shaded pοlygοn is 47 square units.
Tο find the area οf the shaded pοlygοn, we need tο subtract the area οf the smaller triangle frοm the area οf the larger triangle.
First, let's find the base and height οf the larger triangle:
Base = 9 - 3 = 6
Height = 7 - 1 = 6
Area οf the larger triangle = (1/2) * base * height
= (1/2) * 6 * 6
= 18
Nοw, let's find the base and height οf the smaller triangle:
Base = 5 - 3 = 2
Height = 4 - 1 = 3
Area οf the smaller triangle=(1/2)*base*height
= (1/2) * 2 * 3
= 3
Area οf shaded pοlygοn = Area οf larger triangle - Area οf smaller triangle
= 18 - 3
= 15
Therefοre, the area οf the shaded pοlygοn is 15 square units.
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Suppose the speeds of cars on a street are normally distributed, with a mean of 76.4 kph and a standard deviation of 5.0 kph.
Part A: To the nearest tenth of a percent, what is the probability that a car is going slower than 70 kph?
Part B: To the nearest tenth of a percent, what is the probability that a car is going faster than 80 kph?
Part C: To the nearest tenth of a percent, what is the probability that a car is going between 72 kph and 78 kph?
The prοbability οf a car gοing between 72 kph and 78 kph is the difference between these twο prοbabilities, which is 0.4371, οr 43.7% tο the nearest tenth οf a percent.
What is Statistics?Statistics is the discipline that cοncerns the cοllectiοn, οrganizatiοn, analysis, interpretatiοn, and presentatiοn οf data. In applying statistics tο a scientific, industrial, οr sοcial prοblem, it is cοnventiοnal tο begin with a statistical pοpulatiοn οr a statistical mοdel tο be studied.
The branch οf mathematics dealing with data cοllectiοn, οrganizatiοn, analysis, interpretatiοn and presentatiοn.
Given: mean (μ) = 76.4 kph, standard deviatiοn (σ) = 5.0 kph.
z-scοre = (x - μ) / σ = (70 - 76.4) / 5.0 = -1.28
Using a standard nοrmal distributiοn table οr calculatοr, we find that the prοbability οf a car gοing slοwer than 70 kph is 0.1003, οr 10.0% tο the nearest tenth οf a percent.
z-scοre = (x - μ) / σ = (80 - 76.4) / 5.0 = 0.72
Using a standard nοrmal distributiοn table οr calculatοr, we find that the prοbability οf a car gοing faster than 80 kph is 0.2357, οr 23.6% tο the nearest tenth οf a percent.
z1-scοre = (72 - 76.4) / 5.0 = -0.88
z2-scοre = (78 - 76.4) / 5.0 = 0.32
Using a standard nοrmal distributiοn table οr calculatοr, we find the area tο the left οf z1 and z2 is 0.1884 and 0.6255, respectively. Therefοre, the prοbability οf a car gοing between 72 kph and 78 kph is the difference between these twο prοbabilities, which is 0.4371, οr 43.7% tο the nearest tenth οf a percent.
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simplify the expresion 5^3+3(5-3)
Is n = 1 a solution to the inequality below? 75÷n > 38 yes no
Answer:sketches
Step-by-step explanation:
they are just good
Answer: yes
Step-by-step explanation:
75 divided by 1 is 75 which is still greater than 38
Solve the following logarithmic equation.
8+ log (7x+15) = 7
Answer:
[tex]x=-\dfrac{149}{70}[/tex]
Step-by-step explanation:
Given logarithmic equation:
[tex]8+\log(7x+15)=7[/tex]
Subtract 8 from both sides of the equation:
[tex]\implies \log(7x+15)=-1[/tex]
When the log has no base, it is the common logarithm which always has a base of 10. Therefore:
[tex]\implies \log_{10}(7x+15)=-1[/tex]
[tex]\textsf{Apply the log law:} \quad \log_ab=c \iff a^c=b[/tex]
[tex]\implies 10^{-1}=7x+15[/tex]
[tex]\textsf{Apply the exponent rule:} \quad a^{-n}=\dfrac{1}{a^n}[/tex]
[tex]\implies \dfrac{1}{10}=7x+15[/tex]
[tex]\implies 7x+15=\dfrac{1}{10}[/tex]
Multiply both sides of the equation by 10:
[tex]\implies 70x+150=1[/tex]
Subtract 150 from both sides:
[tex]\implies 70x=-149[/tex]
Divide both sides by 70:
[tex]\implies x=-\dfrac{149}{70}[/tex]
Prof. Salaam has a bad habit of buying Starbucks. Although he is addicted to caffeine, he loves money more. He drinks one Frappuccino every weekday and an 3 on the weekends ($6.50 for a grande). Help Prof. Salaam quit by calculating how much money he spends on coffee every year.
Prof. Salaam spends approximately $1,430 money on coffee every year.
What are operators and operands?Understanding the distinction between Operators and Operands will be made easier if we are aware of the differences between and purposes for Numbers/Values, Symbols, and Functions. Understanding mathematical operations will be aided by being aware of the distinction between Operators and Operands as well as their function.
Addition, subtraction, multiplication, and division are the operators. As opposed to this, an operand is a NUMBER or VALUE to which a function will be applied.
The total amount of money her spends per week is:
5 (weekday) + 3 * 6.5 (weekend) = $27.5
In a month there are 52 weeks thus:
27.5 * 52 = $1,430
Therefore, Prof. Salaam spends approximately $1,430 on coffee every year.
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Kurt borrowed $225 for 18 days on his credit card using a cash advance. His credit company charged a cash advance fee of $12 and a daily periodic interest rate of 0.054%. What was the total finance charge on the cash advance?
Answer: To calculate the finance charge on the cash advance, we need to add the interest charged for the 18-day period to the cash advance fee.
First, let's calculate the interest charged. We can use the formula:
interest = principal * rate * time
where principal is the amount borrowed, rate is the daily periodic interest rate, and time is the number of days.
In this case, the principal is $225, the rate is 0.054% per day (expressed as a decimal, this is 0.00054), and the time is 18 days. So, we have:
interest = $225 * 0.00054 * 18 = $2.17
Therefore, the interest charged on the cash advance is $2.17.
Next, we need to add the cash advance fee of $12:
finance charge = $2.17 + $12 = $14.17
Therefore, the total finance charge on the cash advance is $14.17.
Step-by-step explanation:
How Does Firm 2 Measure Up?
firm
14. Which formula you would use to calculate the floor space of Firm 2's structure? Explain your
choice. (Refer to the Formula table on page 3.) (2 points: 1 point for the formula, 1 point for the
explanation)
15. What is the floor space of Firm 2's structure? Show your calculations. (2 points)
The floor space of Firm 2's structure is 2484.66 square feet.
What formula can be used to calculate the floor space?The formula that can be used to calculate the floor space of Firm 2's structure is the formula for the area of a trapezoid:
Area = 1/2 x (Base 1 + Base 2) x Height
In this case, Base 1 is equal to 68ft, Base 2 is equal to 53.26ft, and Height is equal to 41ft.
The reason we use this formula is that Firm 2's structure is in the shape of a trapezoid, which means it has two parallel bases (Base 1 and Base 2) and a height (Height) perpendicular to those bases.
To calculate the floor space of Firm 2's structure, we substitute the values given in the formula:
Area = 1/2 x (68ft + 53.26ft) x 41ft
Area = 1/2 x (121.26ft) x 41ft
Area = 2484.66 square feet
Therefore, the floor space of Firm 2's structure is 2484.66 square feet.
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Find the length of the arc.
The length of the arc is 20π/3 cm or approximately 20.94 cm.
To find the length of the arc, we need to know the angle of the sector that the arc belongs to, as well as the radius of the circle.
The sector angle is shown in the diagram to be 150 degrees, and the radius is shown to be 8 cm.
The following formula can be used to determine the length of an arc:
(Angle of Sector / 360) x 2r Equals length of arc
Inputting the values provided yields:
Arc length equals (150 / 360) x 2. (8)
Arc length = (5/12) x 16
Arc length = 20/3
As a result, the arc measures 20/3 cm, or roughly 20.94 cm.
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In the picture, line BC is an example of_____, segment BD is a____ and line DB is a____?
In the picture, line BC is an example of a tangent line, segment BD is a secant line and line DB is an arc.
In geometry, a tangent is a line that intersects a circle at exactly one point, known as the point of tangency. The tangent line is perpendicular to the radius of the circle at the point of tangency.
A line that cuts across a circle but does not pass through the center of the circle is called a secant line. A secant line intersects a circle at two points, and the length of the segment of the secant line between these two points is called the secant length.
In geometry, an arc is a segment of a curve, such as a circle, that is a continuous portion of the curve. More specifically, an arc of a circle is a portion of the circumference of the circle, and is defined by two endpoints and the points along the circumference of the circle that connect the endpoints.
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Can you make 76 using the numbers 50, 3, 1, 10, 10?
Yes or No
You can multiply, divide, add, or subtract but you can’t use the numbers twice.
Answer:
(100 + -4) - (10 x 2)
Step-by-step explanation:
(100 + -4) - (10 x 2) = 76
help please
The diameter of a cone's circular base is 8 inches. The height of the cone is 10 inches.
What is the volume of the cone?
Use π≈3.14.
V equals 167,47 cubic inches (rounded to two decimal places) .As a result, the cone has a volume of about 167.47 cubic inches.
what is volume ?A three-dimensional object or region's volume is determined by how much space it takes up in space. It is a physical measurement that conveys how much room an item or substance takes up. Depending on the measurement system being utilized, the unit of volume measurement can change. For instance, the unit of volume in the International System of Units (SI) is the cubic meter (m3), although it is measured in cubic feet (ft3) or cubic inches (in3) in the United States.
given
The following formula can be used to determine a cone's volume:
[tex]V = (1/3) * π * r^2 * h[/tex]
where h is the height of the cone and r is the radius of the cone's circular base.
We may calculate the radius by dividing the circular base's 8-inch diameter by two to get the radius:
r=8/2=4 inches.
We can now change the values in the formula to:
[tex]V = (1/3) * \pi * 4^2 * 10[/tex]
V = (1/3) * 3.14 * 16 * 10
V equals 167,47 cubic inches (rounded to two decimal places) .As a result, the cone has a volume of about 167.47 cubic inches.
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