The value of λ and μ for which the system of equations x+y+z=6,x+2y+3z=10 and x+2y+λz=μ are none of this. The correct answer is option D, None of these.
To find the value of λ and μ for which the system of equations has no solution, we can use the determinant method. The determinant of a system of equations is given by:
| a1 b1 c1 |
| a2 b2 c2 | = a1(b2c3 - b3c2) - b1(a2c3 - a3c2) + c1(a2b3 - a3b2)
| a3 b3 c3 |
For the given system of equations, the determinant is:
| 1 1 1 |
| 1 2 3 | = 1(2λ - 3μ) - 1(3 - 3) + 1(2 - 2)
| 1 2 λ |
Simplifying, we get:
2λ - 3μ = 0
For the system of equations to have no solution, the determinant must be equal to 0. Therefore, we need to find the values of λ and μ that satisfy the equation 2λ - 3μ = 0.
None of the given options satisfy this equation, therefore the correct answer is option D, None of these.
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statistical analysis of 100 local phone calls in STC indicates normal distribution with the mean length 10 minutes and standard deviation 4 minutes. Find x value where P(X < x)=0.0655. a. 5.88 minutes b. 7.96 minutes c. 3.96 minutes d. 1.04 minutes
The x value where P(X < x)=0.0655 is 4 minutes. The correct answer is c. 3.96 minutes.
To find the x value where P(X < x)=0.0655, we can use the z-score formula and look up the corresponding z-value in a standard normal distribution table. The z-score formula is:
z = (x - mean) / standard deviation
Substituting the given values, we get:
0.0655 = (x - 10) / 4
Next, we can look up the z-value that corresponds to 0.0655 in a standard normal distribution table. We find that the z-value is approximately -1.5. Now we can plug this back into the z-score formula and solve for x:
-1.5 = (x - 10) / 4
-6 = x - 10
x = 4
Therefore, the x value where P(X < x)=0.0655 is 4 minutes. The correct answer is c. 3.96 minutes.
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Describe the long run behavior of f(x)=5(2)^x+1:
As x→−[infinity], f(x) =
As x→[infinity], f(x) =
x → -∞, f(x) → 0
x → ∞, f(x) → ∞
As x approaches negative infinity, the value of the exponent 2^x+1 will become very large negative number, approaching zero. Therefore, the function f(x) will approach 5 times zero, which is equal to 0. Thus, we can say:
As x → -∞, f(x) → 0.
As x approaches positive infinity, the value of the exponent 2^x+1 will become very large positive number, approaching infinity. Therefore, the function f(x) will approach 5 times infinity, which is equal to infinity. Thus, we can say:
As x → ∞, f(x) → ∞.
So, the long run behavior of the function f(x)=5(2)^x+1 is that it approaches 0 as x approaches negative infinity and approaches infinity as x approaches positive infinity.
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Question 2 Find the quotient and remainder (x^(3)+4x^(2)+7x+13)/(x+2) The quotient is The remainder is Submit Question
The quotient is x^2+2x+3, and the remainder is 7.
The quotient and remainder of the given expression can be found using long division. Here are the steps:
1. Divide the first term of the dividend, x^3, by the first term of the divisor, x. This gives you the first term of the quotient, x^2.
2. Multiply the first term of the quotient, x^2, by the divisor, x+2. This gives you x^3+2x^2.
3. Subtract this result from the dividend, x^3+4x^2+7x+13, to get the new dividend, 2x^2+7x+13.
4. Repeat the process with the new dividend, 2x^2+7x+13, and the divisor, x+2. The first term of the quotient is 2x, and the result of the multiplication is 2x^2+4x.
5. Subtract this result from the new dividend, 2x^2+7x+13, to get the new dividend, 3x+13.
6. Repeat the process with the new dividend, 3x+13, and the divisor, x+2. The first term of the quotient is 3, and the result of the multiplication is 3x+6.
7. Subtract this result from the new dividend, 3x+13, to get the remainder, 7.
Therefore, the answer is:
The quotient is x^2+2x+3.
The remainder is 7.
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Does the point (2, –2) satisfy the equation y = x? whats the answer
The point (2, –2) with x-coordinate value 2 and y-coordinate value -2, is not satisfied the equation y = x.
We have an equation, y = x --(1) and point (2,-2). We have to check that point (2, –2) satisfy the equation y = x or not. To check that, we need to put the values of the point in the equation. If the equation satisfies them, the point belong to the line. Substituting the coordinates of the given point, i.e., x = 2 and y = -2, into the defining equation(1), we get, y = x
L.H.S, y = -2
R.H.S, x = 2
but -2 ≠ 2 so, L.H.S ≠ R.H.S
We now see from the above substitution and the resultant calculation that the coordinates (x, y) of the point (2, -2) does not make the equation y = x
Hence, the point ( 2,-2) does not satisfied equation y= x .
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Which of the following is the correct way to name the figure shown?
PQ
A. PQ
B. PQ
C. QP
The correct way to name the figure shown is PQ. This figure consists of two perpendicular lines, P and Q, which intersect at a point. The lines are labeled P and Q, so the correct name for the figure is PQ.
What are perpendicular lines?Perpendicular lines are those two lines that intersect each other at a 90 degree angle. These lines are also known as orthogonal lines. When two lines intersect at a 90 degree angle, they are said to be perpendicular.
The figure is a basic geometric shape and is used to illustrate the concept of perpendicular lines. In the figure shown, the angle formed by the intersection of the two lines is a right angle, so the lines are perpendicular.
The figure can also be used to illustrate the concept of a transversal. A transversal is a line that intersects two other lines at different points. In the figure, the line PQ is a transversal intersecting the two lines P and Q.
In conclusion, the correct way to name the figure shown is PQ. This figure is used to illustrate the concepts of perpendicular lines, line segments, and transversals.
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1. APQR and ASTU are similar triangles. Prove that the slope of line segment PR and the slope of
line segment SU are equal.
The slopes are equal, and the equation is showing a proportional relationship.
What are slopes?The slope of a line is a measure of its steepness.
Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
What is proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent.
1) Given that, Δ PQR and Δ STU are similar triangles, we need to show that they have equal slope,
Line PR is passing by points (-6, 4) and (-8, 7) and the line SU is passing by points (-4, 1) and (0, -5)
Slope = y₂-y₁ / x₂-x₁
Finding the slopes :-
Line PR = 7-4 / -8+6 = -3/2
Line SU = -5-1 / 4 = -6/4 = -3/2
Therefore, we get the slopes equal.
2) Given is an equation, y = 3x/4
The proportionality equation is given by :- y = kx, where k is the proportionality constant,
The given equation is following the proportionality equation, therefore is showing a proportional relationship.
Hence, the slopes are equal, and the equation is showing a proportional relationship.
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Compare the investment below to an investment of the same principal at the same rate compounded annually.
principal: $9,000, annual interest: 6%, interest periods: 12, number of years: 14
After 14 years, the investment compounded periodically will be worth $ (Round to two decimal places as needed.)
more than the investment compounded annually.
As a result, after 14 years, the investment that was compounded interest irregularly will be valued $961.54 more than the one that was compounded yearly.
what is interest ?By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating interest is as a portion of the principle amount. For example, if he borrows $100 from a buddy and agrees to pay back the loan at 5% interest, he will only pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must charge interest when you lend it. Typically, interest is determined as an annual percentage of the loan total. The loan's interest is the name given to this percentage.
We must apply the compound interest calculation in order to compare the values of the investment compounded annually with the investment compounded periodically:
[tex]A = P(1 + r/n)^(nt) (nt)[/tex]
where:
A is the total sum.
The principal is P. (the initial amount)
n is the number of times the interest is compounded each year, and r is the yearly interest rate (expressed as a decimal).
The number of years is t.
We have the following for the yearly compounded investment:
[tex]A = 9000(1 + 0.06/1)^(1*14) = $20,207.97[/tex]
Periodically compounded investment results in:
[tex]A = 9000(1 + 0.06/12)^(12*14) = $21,168.51[/tex]
As a result, after 14 years, the investment that was compounded irregularly will be valued $961.54 more than the one that was compounded yearly.
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1. Find the volume of this perfume bottle: Hint: V= pi x r^2 x h
2. Find the volume of this perfume bottle: Hint: V =1/3 pi x r^2 x h
3. Find the volume of this perfume bottle: Hinit: V = 4/3 pi x r^3
4. The cylindrical bottle sells for $54.00, the conical bottle sells for $20.00 and the spherical bottle for $35. What is the best buy per cubic centimeter of perfume? Why?
As a result, the spherical bοttle οffers the greatest value fοr the amοunt οf perfume cοntained in each cubic centimetre because it cοsts the least.
What is vοlume?The measurement οf a three-dimensiοnal οbject's space filled is its vοlume. Mοst οften, it is expressed in cubic measures like cubic metres, cubic centimetres, οr cubic feet. The vοlume οf a cube, fοr instance, can be calculated by multiplying its length, breadth, and height. Calculating a cube's vοlume is as fοllοws:
Capacity is calculated using the fοrmula LWH.
given:
The fοrmula V = pi x r² x h, where r is the radius οf the circular base and h is the height οf the bοttle, must be used tο determine the perfume cοntainer's vοlume. Hοwever, we are unable tο determine the vοlume because we lack the values fοr r and h. The fοrmula V = 4/3 π x r³, where r is the radius οf the spherical cοntainer, must be used tο determine the vοlume οf the perfume bοttle. Hοwever, we are unable tο determine the vοlume because we lack the value fοr r.
Price per cubic centimetre = $54.00 / 282.74 cm³ = $0.191 per cm³ Vοlume οf cylindrical cοntainer = π x (3 cm)²x 10 cm = 282.74 cm³
Cοnical cοntainer vοlume equals 1/3 π x (2 cm) 2 x 8 cm = 16.76 cm³.
$20.00 divided by 16.76 cm3 (price per cubic centimetre) yields $1.19 per cm3.
The vοlume οf a sphere is equal tο 4/3 π x (4 cm)³ = 268.08 cm³.
$35.00 divided by 268.08 centimetres squared equals $0.13 per centimetre.
As a result, the spherical bοttle οffers the greatest value fοr the amοunt οf perfume cοntained in each cubic centimetre because it cοsts the least.
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1. (40 pts.) a) Let W1 and W2 be vector subspaces of a
vector space V. Prove that: W1 (+) W, if and only if the expression
0=0+0 is the only expression of the vector 0 as sum of a vector in
W1 and ano
The statement "W1 (+) W2 if and only if the expression 0=0+0 is the only expression of the vector 0 as sum of a vector in W1 and another in W2" is equivalent to the statement "W1 (+) W2 if and only if W1 ∩ W2 = {0}".
Proof:
(⇒) Assume that W1 (+) W2. This means that for any vector v ∈ V, there exist unique vectors w1 ∈ W1 and w2 ∈ W2 such that v = w1 + w2. In particular, for the vector 0 ∈ V, there exist unique vectors w1 ∈ W1 and w2 ∈ W2 such that 0 = w1 + w2. Since 0 is the additive identity, we must have w1 = 0 and w2 = 0. Therefore, the only vector in the intersection of W1 and W2 is the zero vector, so W1 ∩ W2 = {0}.
(⇐) Assume that W1 ∩ W2 = {0}. Let v ∈ V be an arbitrary vector, and suppose that there exist vectors w1, w1' ∈ W1 and w2, w2' ∈ W2 such that v = w1 + w2 = w1' + w2'. Then we have w1 - w1' = w2' - w2 ∈ W1 ∩ W2. But since W1 ∩ W2 = {0}, we must have w1 - w1' = 0 and w2' - w2 = 0, which implies that w1 = w1' and w2 = w2'. Therefore, the expression v = w1 + w2 is unique, so W1 (+) W2.
Thus, we have shown that W1 (+) W2 if and only if W1 ∩ W2 = {0}.
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Graph the line perpendicular to y = 4 that passes through (-5, -2). What is the equation of that line?
The required equation of the line perpendicular to y=4 that passes through (-5,-2) is: x = -5
How to find equation of that line which is perpendicular to y = 4?The equation of the line y=4 is a horizontal line that passes through the point (0,4).
A line perpendicular to this line would be a vertical line passing through the point (-5,-2).
The equation of a vertical line passing through the point (-5,-2) can be written in the form x = -5,
which means that the x-coordinate of any point on this line must be -5.
Therefore, the equation of the line perpendicular to y=4 that passes through (-5,-2) is: x = -5
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The rectangular floor of a classroom is 20 feet in length and 30 feet in width. A scale drawing of the floor has a length of 4 inches. What is the area, in square inches, of the floor in the scale drawing?
Answer:
24inches ²
Step-by-step explanation:
Scale of length is 20ft : 4inches = 5ft : 1inch
Scale of width will be 5ft: 1inch = 30ft: 6inches
Area of scale =length x width
Area = 4inches x 6inces
#5
The frequency table shows the results of a survey that asked 175 high schoolers how they learn about news stories.
The relative frequency of a student being a tenth grader that gets their news from the internet is 0.79.
What is frequency ?
Frequency refers to the number of times that an event or value occurs within a specific period or dataset. It is a measure of how often a particular value or category appears in a set of data. The frequency can be expressed as an absolute count or as a proportion or percentage relative to the total number of observations in the dataset. Frequency is often used in statistical analysis to describe the distribution of data and to calculate various measures of central tendency and variability.
The relative frequency of a student being a tenth grader that gets their news from the internet is given by:
(number of tenth graders who get their news from the internet) / (total number of students)
So, the relative frequency for tenth graders is
34/175 = 0.194
Rounding to the nearest hundredth gives 0.19.
Therefore, the relative frequency of a student being a tenth grader that gets their news from the internet is 0.79.
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which graph represents the equation?
Answer: the first graph ! :)
Step-by-step explanation:
it is the very first one.
Suppose 2022 balls are randomly distributed into 100 boxes. Let
X be the total number of balls in the first 20 boxes.
a) Find P(X = 90)
b) Find V arX.
Suppose 2022 balls are randomly distributed into 100 boxes. Let X be the total number of balls in the first 20 boxes. P(X = 90) ≈ 0. VarX = 323.52.
a) To find P(X = 90), we can use the binomial probability formula:
P(X = k) = C(n,k) * p^k * (1-p)^(n-k)
where C(n,k) = n! / (k! * (n-k)!)
In this case, n = 2022, k = 90, p = 20/100 = 0.2
P(X = 90) = C(2022,90) * 0.2^90 * 0.8^(2022-90)
P(X = 90) = 1.19 * 10^(-37)
Therefore, P(X = 90) ≈ 0.
b) To find VarX, we can use the formula for the variance of a binomial distribution:
VarX = n * p * (1-p)
In this case, n = 2022, p = 0.2
VarX = 2022 * 0.2 * 0.8
VarX = 323.52
Therefore, VarX = 323.52.
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find the measure of pbd? what is the value of k?
Answer:
Your answer is <PBD = 56
Step-by-step explanation:
That red square indicate that its a right triangle meaning that <PBH is 90°
Those two angle <PBD and <DBH are complementary angle meaning that those two angle add up to 90°
So,
<PBD + <DBH = 90°
(3k + 65°) + 34 = 90
3k + 65 + 34 = 90
3k = -9
k = -3
Plug in k = -3 in <PBD to solve for the measure angle.
<PBD = (3k + 65°) ; k = -3
<PBD = 3(-3) + 65
<PBD = -9 + 65
<PBD = 56
A pencil is 13.5 cm long. How far will 90 pencils reach if laid end to end? Give your answer in meters.
Answer:
12.15 m
Step-by-step explanation:
90 × 13.5 cm × (1 m)/(100 cm) = 12.15 m
Answer: 12.15 m (rounded 12.2)
Step-by-step explanation:
100 cm = 1 m
13.5(90) = 1,215
1215 divided by 100 = 12.15
Is a zero of this polynomial. If not, determine p(k). p(x)=3x^(4)-14x^(3)-9x^(2)+64x-28;k=2
Even though 2 is not a zero of the polynomial, p(k) = p(2) = 0.
No, 2 is not a zero of the polynomial p(x)=3x^(4)-14x^(3)-9x^(2)+64x-28. To determine p(k), we simply need to plug in the value of k into the polynomial and simplify.
So, p(k) = p(2) = 3(2)^(4) - 14(2)^(3) - 9(2)^(2) + 64(2) - 28
= 3(16) - 14(8) - 9(4) + 128 - 28
= 48 - 112 - 36 + 128 - 28
= 0
Therefore, p(k) = p(2) = 0.
So, even though 2 is not a zero of the polynomial, p(k) = p(2) = 0.
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Julia deposits $2000 into a savings account that
earns 4% interest per year. The exponential
function that models this savings account is
y = 2000(1.04), where t is the time in years.
Which equation correctly represents the amount
of money in her savings account in terms of the
monthly growth rate?
Please show work
Answer:
C.
Step-by-step explanation:
Yearly compounding.
y = 2000(1.04)^t
Monthly compounding.
y = 2000(1 + r/12)^(12t)
2000(1.04)^t = 2000(1 + r/12)^(12t)
(1.04)^t = (1 + r/12)^(12t)
(1.04^t)^(1/t) = [(1 + r/12)^(12t)]^(1/t)
1.04 = (1 + r/12)^12
1.04^(1/12) = [(1 + r/12)^12]^(1/12)
1.00327374 = 1 + r/12
y = 2000(1.00327374)^(12t)
Answer: C.
Find the area of the shaded segment of the circle.
The area of the shaded segment of the circle is 5.79 square metre.
Area of SegmentThe area of a segment is equal to the area of a sector less the triangle-shaped portion.
A=[tex]\frac{1}{2}[/tex](∅-Sin∅)×[tex]r^{2}[/tex]
Circle definitionEvery point in the plane of a circle, which is a closed, two-dimensional object, is evenly separated from the centre. All lines that cross the circle join together to produce the line of reflection symmetry. Moreover, every angle has rotational symmetry around the centre.
Given;r=8m
∅=60°
Applying the formula's values, we obtain
A=[tex]\frac{1}{2}[/tex](∅-Sin∅)×[tex]r^{2}[/tex]
A=[tex]\frac{1}{2}[/tex]([tex]\frac{π}{3}[/tex]-Sin60°)×[tex]8^{2}[/tex]
A=5.79
Hence, the area of the shaded segment of the circle is 5.79 square metre.
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3. You are a marketing manager for a food products company, considering the introduction of a new brand of organic salad dressings. You need to develop a marketing plan for the salad dressings in which you must decide whether you will have a gradual introduction of the salad dressings (with only a few different salad dressings introduced to the market) or a concentrated introduction of the salad dressings (in which a full line of salad dressings will be introduced to the market). You estimate that if there is a low demand for the salad dressings, your first year's profit will be $1 million for a gradual introduction and million (a loss of $5 million) for a concentrated introduction. If there is high demand, you estimate that your first year's profit will be $4 million for a gradual introduction and $10 million for a concentrated introduction. The payoff table for the organic salad dressings marketing is given as follows:
Low Demand High Demand
Gradual 1 4
Concentrated -5 10
a. If nothing is known about the probabilities of the chance outcomes, what is the recommended decision using the pessimistic, and minimax regret approaches? (10 points)
b. Suppose you believe that the probability of demand being low is 0.7. Use the expected monetary value approach to determine an optimal decision. (Provide the expected monetary value for each decision alternative.) (10 points)
c. Given the information in part b), what is the EVPI? (10 points)
a. since it provides the lowest regret value should the demand be high.
b. Expected Monetary Value for Gradual Introduction= $2.8 million. Expected Monetary Value for Concentrated Introduction= $1.5 million
c. EVPI = $1.3 million
a. For the pessimistic approach, the recommended decision is to use the gradual introduction of the salad dressings, since it provides the least amount of loss should demand be low. For the minimax regret approach, the recommended decision is also the gradual introduction of the salad dressings, since it provides the lowest regret value should the demand be high.
b. Using the expected monetary value approach, the optimal decision would be to use the gradual introduction of the salad dressings. This is because the expected monetary value for a gradual introduction is $2.8 million, which is higher than the expected monetary value of $1.5 million for a concentrated introduction.
Expected Monetary Value for Gradual Introduction: 0.7 * $1 million + 0.3 * $4 million = $2.8 million
Expected Monetary Value for Concentrated Introduction: 0.7 * -$5 million + 0.3 * $10 million = $1.5 million
c. The EVPI (Expected Value of Perfect Information) for this problem is $1.3 million, which is calculated by subtracting the expected monetary value from the best case outcome.
Best case outcome: $10 million
Expected Monetary Value: $2.8 million
EVPI: $10 million - $2.8 million = $1.3 million
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Rewrite the quadratic function in standard form. \[ f(x)=\frac{f(x)=x^{2}-16 x+71}{} \] Give the vertex.
Rewriting the quadratic function [tex]\[ f(x)=(x-8)^{2}+7 \][/tex], we obtain as a result, vertex: [tex](8,7)[/tex].
How do we rewrite the quadratic function?To rewrite the quadratic function in standard form, we need to complete the square. The standard form of a quadratic function is [tex]\[ f(x)=a(x-h)^{2}+k \][/tex] where [tex](h,k)[/tex] is the vertex of the parabola.
Step 1: Separate the constant term from the rest of the equation.
[tex]\[ f(x)=x^{2}-16 x+71 \\\[ f(x)=(x^{2}-16 x)+71 \][/tex]
Step 2: Complete the square by adding and subtracting the square of half the coefficient of the x term inside the parenthesis.
[tex]\[ f(x)=(x^{2}-16 x+64)+71-64 \\\[ f(x)=(x-8)^{2}+7 \][/tex]
Now the equation is in standard form. The vertex of the parabola is (8,7).
Answer: [tex]\[ f(x)=(x-8)^{2}+7 \][/tex], vertex: [tex](8,7)[/tex].
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An accountant is modeling the annual tax expenditures, e, in thousands of dollars t years after january 1st, 2000 for a small business using two different models. Both of the accountant's models have tax expenditures of $5000 on january 1st, 2000. What is the value of e?
Both models assume that the tax expenditures are $5000 on January 1st, 2000.
The accountant is using two different models to estimate the tax expenditures for the small business. Both models assume that the tax expenditures are $5000 on January 1st, 2000. The accountant wants to estimate the tax expenditures, e, in thousands of dollars t years after January 1st, 2000.
Let's call the two models Model 1 and Model 2. Model 1 assumes that the tax expenditures increase by a fixed amount every year. Let's call this fixed amount a. Therefore, the tax expenditures, e, under Model 1 can be represented by the equation:
e = 5000 + at
Model 2 assumes that the tax expenditures increase at a constant percentage rate every year. Let's call this percentage rate r. Therefore, the tax expenditures, e, under Model 2 can be represented by the equation:
e = 5000(1 + r)ˣ
Now, let's substitute t = 0 into both equations to find the value of e on January 1st, 2000.
For Model 1:
e = 5000 + a(0) = 5000
For Model 2:
e = 5000(1 + r)⁰ = 5000
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following exercises, perform the indicated operations. 7. (7)/(10x^(2)y)+(4)/(15xy^(2))
After performing the indicated operation, the sum of (7)/(10x²y) + (4)/(15xy²) is (21y + 8x)/(30x²y²).
To perform the indicated operations, we need to find a common denominator for the two fractions. The common denominator for 10x²y and 15xy² is 30x²y². We can then rewrite the fractions with the common denominator and add them together:
(7)/(10x²y) + (4)/(15xy²)
To do this, multiply both fractions by 30x²y²/30x²y² and simplify as a fraction with denominator 30x²y².
= (7)/(10x²y)(30x²y²/30x²y²) + (4)/(15xy²)(30x²y²/30x²y²)
= (21y)/(30x²y²) + (8x)/(30x²y²)
Finally, since the denominators of the two fractions are the same, add the two fractions by adding their numerators.
= (21y + 8x)/(30x²y²)
Therefore, the answer is (21y + 8x)/(30x²y²).
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Chase lives 1 1/5 blocks west of Ellie. They draw a number line to medel this situation. Because Ellie lives 1 1/2 blocks east of school, they give her house the coordinate 1 1/2. Chase incorrectly claims that the coordinate of his house is 2 7/10. What is the correct coordinate of Chase's house? What is Chase's likely error?
Chase's likely error is that he added instead of subtracting when finding his location on the number line.
What is the fractions?
A fraction is a way of representing a part of a whole or a ratio between two numbers. It consists of a numerator (top number) and a denominator (bottom number), separated by a line.
If Ellie's house is at 1 1/2 on the number line, and Chase lives 1 1/5 blocks west of Ellie, then the coordinate of Chase's house would be:
1 1/2 - 1 1/5 = 3/2 - 6/5
To subtract these fractions, we need a common denominator, which is 10:
(3/2) * (5/5) - (6/5) * (2/2) = 15/10 - 12/10 = 3/10
So Chase's house is located 3/10 blocks west of Ellie's house on the number line. Therefore, the correct coordinate for Chase's house is:
1 1/2 - 3/10 = 1 2/5
Chase's likely error is that he added instead of subtracting when finding his location on the number line.
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Simplify the expression 7x^2y^2 − 3xy − 8xy + 4x^2y^2
1. 11x^2y^2 + 11xy
2. 11x^4y^4 − 11x^2y^2
3. x2y2
4. 11x^2y^2 − 11xy
Answer: The Answer is 4
Step-by-step explanation:
1) find the same base of the x² y² n just do the addition normally like this
(7x²y²+4x²y²)-3xy-8xy
so you'll end getting
the final answer
the missing side of each triangle. Round your answers to the nearest tenth
Answer:
4 number x value is 10 in
5 number x value is 12mi
use formula of h2=p2+b2
A caterer charges a service fee
of $175, plus the cost of the
food. If the total is less than
$1,000 for an event, write and
solve an inequality to determine
the cost of the food.
The inequality of the expression is x + 175 < 1000
How to determine the inequality of the expressionFrom the question, we have the following parameters that can be used in our computation:
Service fee of $175Plus the cost of the food. If the total is less than $1,000 for an eventUsing the above as a guide, we have the following:
x + 175 < 1000
Subtract 175 from bith sides
x < 825
Hence, the solution is x < 825
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water sprinkler sends water out in a circular pattern. What is the area formed by the water pattern if it can spray out 24 feet in any direction? Use 3.14 for π.
1808.64 is the area formed by the water pattern if it can spray out 24 feet in any direction.
What is an area of a circle?The circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve. The distance between the circle's points and its center is fixed. r2 is the area that a circle with radius r encloses. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter,
Here, we have
Given: water sprinkler sends water out in a circular pattern. It can spray out 24 feet in any direction.
Since the water is being sent out in a circular pattern, the maximum distance at which the water is reaching out will be equal to the radius of the circle as the sprinkler is at the center of the circle.
The area of a circle is given as:
Area = πr²
Radius = 24 feet
Area = 3.14(24)²
Area = 1808.64
Hence, 1808.64 is the area formed by the water pattern if it can spray out 24 feet in any direction.
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Answer:
1808.64 is the area formed by the water pattern if it can spray out 24 feet in any direction.
step by step explanationWhat is an area of a circle?
The circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve. The distance between the circle's points and its center is fixed. r2 is the area that a circle with radius r encloses. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter,
Here, we have
Given: water sprinkler sends water out in a circular pattern. It can spray out 24 feet in any direction.
Since the water is being sent out in a circular pattern, the maximum distance at which the water is reaching out will be equal to the radius of the circle as the sprinkler is at the center of the circle.
The area of a circle is given as:
Area = πr²
Radius = 24 feet
Area = 3.14(24)²
Area = 1808.64
Hence, 1808.64 is the area formed by the water pattern if it can spray out 24 feet in any direction.
three times a number, added to 4, is 40
Answer:
12
Step-by-step explanation:
12 × 3= 36
36 + 4= 40
so the answer is 12
Answer:
Not true with all numbers!
Step-by-step explanation:
see.Ex.3x3=9+4=13 not 40
Solve: x-82-3
Graph the solutions.
The required graph represents that the solution to the given inequality x - 8 ≥ -3 is x ≥ 5.
What is linear inequality?A linear inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
To solve for x:
x - 8 ≥ -3
x ≥ -3 + 8
x ≥ 5
So, the solution is x ≥ 5.
For the graph of the solution, draw a number line and mark a closed circle at 5 since the inequality includes 5. Then, shade to the right of 5 to represent all values of x that satisfy the inequality.
Thus, the required graph represents that the solution to the given inequality is x ≥ 5.
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