Solve the equation using either addition or substitution. Show all your work
Answers
Answer:
(x1, y1) = (1, 3)
(x2, y2) = (4, 12)
Step-by-step explanation:
y= x^2 - 4
y= 5x - 8
(substitute the value for y)
x^2 - 4 = 5x - 8
(solve the equation)
x = 1
x = 4
(substitute the values)
y = 5 × 1 - 8
y = 5 × 4 - 8
(solve the equations)
y = -3
y = 12
( the possible solutions are)
x1, y1 = 1, -3
x2, y2 = 4, 12
(check the solutions)
-3 = 1^2 - 4
-3 = 5 × 1 - 8
12 = 4^2 - 4
12 = 5 × 4 - 8
(simplify)
-3 = -3
-3 = -3
12 = 12
12 = 12
(the ordered pairs are the solutions)
Related Questions
The test statistic of z = 2.58 is obtained when testing the claim that p = 0.85. Find the P-value. (Round the answer to 4 decimal places and enter numerical values in the cell)
Answers
Given z-score is z = 2.58 and the null hypothesis isH0: p = 0.85, where p is the true proportion, and we need to find the p-value.
We know that for a two-tailed test, the p-value is the probability that a z-score is greater than or equal to the absolute value of the calculated z-score or less than or equal to its negative value. So, the p-value for a two-tailed test is: p-value = P(z ≥ 2.58) + P(z ≤ -2.58) ..............(1) Here, z = 2.58 represents the upper critical value, and the negative of it is the lower critical value (z = -2.58)
As the given hypothesis is a two-tailed test, we need to calculate the probabilities for both critical values. From the standard normal distribution table, the probabilities for these critical values are:
P(z ≥ 2.58) = 0.0049 (approx.) P(z ≤ -2.58) = 0.0049 (approx.)
Substituting these values in equation (1), we get: p- value = 0.0049 + 0.0049 p-value = 0.0098Hence, the p-value is 0.0098 (approx.)
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Evaluate : ab−5c+b
for a = 12, b = 3 and c = - 4
Answers
Answer:
59
Step-by-step explanation:
[tex](12*3)-5*(-4)+3=59[/tex]
The mean of a normal probability distribution is 400 pounds. The standard deviation is 10 pounds.
a. What is the area between 415 pounds and a mean of 400 pounds?
b. What is the area between the mean and 395 pounds?
c. What is the probability of selecting a value at random and discovering that it has a value of less than 395 pounds?
Answers
The probability of selecting a value at random and discovering that it has a value of less than 395 pounds is 0.3085.
a. The area between 415 pounds and a mean of 400 pounds is:
0.9332 - 0.5 = 0.4332.
b. The area between the mean and 395 pounds is:
0.5 - 0.3085 = 0.1915
c.The probability of selecting a value at random and discovering that it has a value of less than 395 pounds is 0.3085.
Given the mean of a normal probability distribution as 400 pounds and the standard deviation as 10 pounds.
We have to calculate the area between 415 pounds and a mean of 400 pounds, the area between the mean and 395 pounds, and the probability of selecting a value at random and discovering that it has a value of less than 395 pounds.
a. What is the area between 415 pounds and a mean of 400 pounds?
The Z-score can be calculated as follows:
Z = (x - μ) / σ
= (415 - 400) / 10
= 1.5
From the Z-table, the area to the left of 1.5 is 0.9332.
Therefore, the area between 415 pounds and a mean of 400 pounds is:
0.9332 - 0.5 = 0.4332.
b. What is the area between the mean and 395 pounds?
The Z-score can be calculated as follows:
Z = (x - μ) / σ
= (395 - 400) / 10
= -0.5
From the Z-table, the area to the left of -0.5 is 0.3085.
Therefore, the area between the mean and 395 pounds is:
0.5 - 0.3085 = 0.1915.
c. What is the probability of selecting a value at random and discovering that it has a value of less than 395 pounds?
The Z-score can be calculated as follows:
Z = (x - μ) / σ
= (395 - 400) / 10
= -0.5
From the Z-table, the area to the left of -0.5 is 0.3085.
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What is the solution set for -4m ≥ 96?
m ≥ -384
m ≤ -24
m ≤ -384
m ≥ -24
Answers
Answer:
Step-by-step explanation:
-4m≥96
-m≥24
m≤-24
You pick one card from each set and find the sum. How many different sums are possible? 4 5 6 5 6 7 1 2
Answers
There are a total of 9 possible sums. Suppose, the cards in the first set are 4, 5, and 6.
Similarly, the cards in the second set are 5, 6, and 7. A total of nine cards are there. If we choose one card from the first set and one card from the second set, then we get a total of nine possible pairs.
Hence, the sum of these pairs can be 4 + 5, 4 + 6, 4 + 7, 5 + 5, 5 + 6, 5 + 7, 6 + 5, 6 + 6, and 6 + 7. Therefore, there are nine possible sums possible.
Additionally, there are three possibilities in the first set (4, 5, and 6) and three possibilities in the second set (5, 6, and 7).
This means that there are 3 × 3 = 9 possible pairs of cards that we can choose, so there are 9 possible sums.We can list all of these sums as follows:4 + 5 = 96 + 5 = 116 + 5 = 116 + 6 = 127 + 5 = 127 + 6 = 137 + 7 = 14. Therefore, there are a total of 9 possible sums.
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Juan has a profitable web business of selling T-shirts priced at $25 each. His demand is pretty steady throughout the year (his website is up and running 365 days a year), approximately normally distributed with a mean of 30 T-shirts/day and a standard deviation of 10 T-shirts/day. He has a supplier in China that charges him $5 per T-shirt T and a flat rate of $150 every time he places an order. Orders take exactly 50 days to arrive by container ship. His calculates his annual per unit holding costs at 20% of the wholesale cost of T-shirts. a) What type of inventory management problem is this? Explain your answer. i) Newsvendor (single period) model ii) EOQ model with continuous demand distribution 111) EOQ model with discrete demand distribution b) Calculate how many T-shirts he should order from his China supplier at a time. c) Calculate the level at which he should reorder T-shirts from China to experience at most a 10% chance of a stocking out. a T-shirts, Juan should place an order for d) Fill in: When inventory drops to more T-shirts.
Answers
Juan should order approximately 1,813 T-shirts from his China supplier at a time.
How to explain the informationThis inventory management problem can be categorized as the EOQ (Economic Order Quantity) model with continuous demand distribution. In this case, the demand for T-shirts is approximately normally distributed, and the EOQ model assumes a continuous demand pattern.
In order to calculate the optimal order quantity (EOQ), we can use the following formula:
EOQ = ✓((2 * D * S) / H)
where:
D = Annual demand (mean) = 30 T-shirts/day * 365 days/year = 10,950 T-shirts/year
S = Ordering cost per order = $150
H = Holding cost per unit = 20% of wholesale cost = 0.2 * $5 = $1
EOQ = ✓((2 * 10,950 * 150) / 1)
= ✓(3,285,000)
≈ 1,812.99
Therefore, Juan should order approximately 1,813 T-shirts from his China supplier at a time.
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Determine if the following systems is a) Linear b) Time-invariant c) Causal, Justify your answer. y(0) = x(t)sinwet
Answers
The given system y(0) = x(t)sin(wt) is linear, time-invariant, and causal. It satisfies the properties of superposition and homogeneity, exhibits the same time shift in the output as in the input, and the output at any given time depends only on the current and past values of the input.
a) Linearity: A system is linear if it satisfies the properties of superposition and homogeneity. In this case, the system is linear because it satisfies both properties. The input signal x(t) can be scaled or added together, and the corresponding output y(t) will also be scaled or added accordingly.
b) Time-invariance: A system is time-invariant if a time shift in the input signal results in the same time shift in the output signal. In this case, the system is time-invariant because shifting the input signal x(t) by a time delay will result in the same time delay in the output signal y(t).
c) Causality: A system is causal if the output at any given time depends only on the current and past values of the input. In this case, the system is causal because the output y(t) at any time t depends only on the values of the input x(t) for t' ≤ t.
In conclusion, the given system y(0) = x(t)sin(wt) is linear, time-invariant, and causal based on the justification provided above.
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A small internet trading company estimates that each network blackout results in a $500 loss. Compute expectation and variance of this company’s daily loss due to blackouts.
x = 0, 1, 2
Px = 0.7, 0.2, 0.1
Answers
The expectation (mean) of the company's daily loss due to blackouts is $200, and the variance is $350.
To compute the expectation of the company's daily loss, we multiply each possible loss value by its corresponding probability and sum them up. In this case, we have three possible loss values (0, 1, and 2) with their respective probabilities (0.7, 0.2, and 0.1). Multiplying each loss value by its probability and summing them gives us the expected value of $200.
To calculate the variance, we need to find the squared differences between each possible loss value and the expected value, multiply them by their respective probabilities, and sum them up. Squaring the differences ensures that negative differences do not cancel out positive differences. In this case, the variance is calculated as (0 - 200)^2 * 0.7 + (1 - 200)^2 * 0.2 + (2 - 200)^2 * 0.1, resulting in a variance of $350.
The expectation and variance provide useful measures of the central tendency and variability, respectively, of the company's daily loss due to blackouts.
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Find the missing side and round to the nearest tenth
Answers
1) 1/3(x+3)+1/6=1/2(x-1)-(x-3)
Answers
Answer:
x= 8/5
Step-by-step explanation:
Let's solve your equation step-by-step.
1
3
(x+3)+
1
6
=
1
2
(x−1)−(x−3)
Step 1: Simplify both sides of the equation.
1
3
(x+3)+
1
6
=
1
2
(x−1)−(x−3)
1
3
(x+3)+
1
6
=
1
2
(x−1)+−1(x−3)(Distribute the Negative Sign)
1
3
(x+3)+
1
6
=
1
2
(x−1)+−1x+(−1)(−3)
1
3
(x+3)+
1
6
=
1
2
(x−1)+−x+3
(
1
3
)(x)+(
1
3
)(3)+
1
6
=(
1
2
)(x)+(
1
2
)(−1)+−x+3(Distribute)
1
3
x+1+
1
6
=
1
2
x+
−1
2
+−x+3
(
1
3
x)+(1+
1
6
)=(
1
2
x+−x)+(
−1
2
+3)(Combine Like Terms)
1
3
x+
7
6
=
−1
2
x+
5
2
1
3
x+
7
6
=
−1
2
x+
5
2
Step 2: Add 1/2x to both sides.
1
3
x+
7
6
+
1
2
x=
−1
2
x+
5
2
+
1
2
x
5
6
x+
7
6
=
5
2
Step 3: Subtract 7/6 from both sides.
5
6
x+
7
6
−
7
6
=
5
2
−
7
6
5
6
x=
4
3
Step 4: Multiply both sides by 6/5.
(
6
5
)*(
5
6
x)=(
6
5
)*(
4
3
)
x=
8
5
I need help with this question ( see image). Please show workings.
Answers
Answer:
13. (a) 120°, 120°, (b) 8.94 cm14. (a) 17.9 cm, (b) 22.4 cmStep-by-step explanation:
Refer to the attached sketch (not to scale)Question 13(a) The center of the circle is also the circumcenter of the triangle PQR.
Since ΔPQR is equilateral, all sides are equal, therefore opposite angles are also congruent:
∠POQ ≅ ∠QOR ≅ PORSum of the three angles is 360° as cover the full circle.
Each angle measure is:
∠POQ = ∠QOR = ∠POR = 360°/3 = 120°(b) Each side is 16 cm and the radius is 12 cm.
The distance of the midpoint M of PQ from the center O is perpendicular bisector of ΔPOQ.
The segment MO is:
MO² = PO² - PM² = PO² - (PQ/2)²MO² = 12² - (16/2)² = 80MO = √80 = 8.94 cm (rounded)Question 14ΔXYZ is isosceles with:
XY = XZ = 20 cmYZ = 18 cm(a) The altitude of ΔXYZ is a perpendicular bisector of YZ. h = XM is the altitude
Find h:
h² = XZ² - ZM² = XZ² - (ZY/2)²h² = 20² - (18/2)² = 319h = √319h = 17.9 cm (rounded)(b) Note the ∠ZXM is half of the ∠ZOM as both the angles intercept half of the arc ZY and ∠ZOM is a central angle.
Find ∠ZXM:
sin ∠ZXM = ZM/ZX = 9 / 20m∠ZXM = arcsin (9/20) = 26.7° (rounded)Find ∠ZOM:
m∠ZOM = 2*m∠ZXM = 2*26.7 = 53.4°Find the measure of the radius:
sin ∠ZOM = ZM/rsin 53.4° = 9/rr = 9 / sin 53.4°r = 11.2 cm (rounded)Find the measure of the diameter:
d = 2r = 2*11.2 cm = 22.4 cm• What is the diameter of the circle?
What is the circumference of the circle
What is the area of the circle
Answers
Answer:
Radius = r
Diameter = 2r
Circumference = 2πr
Area = πr²
a diameter of a circle is a line drawn through the center of a circle.
yo please help its for a grade!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
(1, 2.5 (or 3/2))
Step-by-step explanation:
It's the point the two lines meet
You believe that a corporation's dividends will grow 5% on average into the foreseeable future. If the company's last dividend payment was $5 what should be the current price of the stock assuming a 12% required return?
Answers
The calculated value of the current price of the stock is $75
How to calculate the current price of the stockFrom the question, we have the following parameters that can be used in our computation:
Growth = 5%
Required return = 12%
Last dividend payment = $5
The dividend is calculated as
D = Last dividend payment * (1 + Growth )
So, we have
D = 5 * (1 + 5%)
Evaluate
D = 5.25
the current price of the stock is calculated as
Price = D/(r - g)
So, we have
Price = 5.25/(12% - 5%)
Evaluate
Price = 75
Hence, the current price of the stock is $75
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The perimeter of a square is 28 cm. Find its area and the length of its diagonal.
help me
Answers
Step-by-step explanation:
area: 28/4=7
7x7=49
diagonal=square root 7²+7²
9.89949
9.90
hope it can help you
Sam raked 3 bags of leaves in 18 minutes. If he continues to work at the same rate, how long will it take him to rake 7 bags of leave ? PLEASE HELP
Answers
Answer:
Step-by-step explanation:
hope it helps make brainliest
Answer:
42 minutes
Step-by-step explanation:
18/3= 6
6*7=42
A car dealership has 180 cars on their lot. If they increase their inventory by 25%, how many cars will be on the lot?
Answers
Answer:
There will be 225 cars on the lot.
A car dealership has 180 cars on their lot. If they increase their inventory be 25%, how many cars will be on the lot?
25/100 * 180
= 5 * 9 = 45
Therefore:
180 + 45 = 225 cars
Answer:
There will be 225 cars on the lot.
PLEASE HELP THIS IS PYTHAGOREAN THEORM 3D
I MARK THE BRANILIEST
What is the vertical height, hh
Round your answer to the nearest tenth.
The height is
units
Answers
Answer:
The height is 6.3
Step-by-step explanation:
Pythagorean Theorm: a² + b² = c²
5² + b² = 8²
25 + b² = 64
b² = 39
b = 6.2449979984
Don't understand. Help please?
Answers
Answer:
Length is 138 ft, area is 412 ft
Step-by-step explanation:
The length is determined by the perimeter, so add both side of the perimeter together, and you have your length. Area is determined by perimeter + Length, to add both sides of perimeter and length and you get 412 ft.
A globe company currently manufactures a globe that is 16 inches in diameter. If the dimensions of the globe were reduced by half, what would its volume be? Use 3.14 for π and round your answer to the nearest tenth.
682.7 in^3
2143.6 in^3
85.3 in^3
267.9 in^3
Answers
If dimensions of the globe that is 16 inches in diameter were reduced by half, then its volume would be [tex]$V= 267.9 \text{ in}^{3}$[/tex]
What is volume ?The volume of an object is a measure of the amount of space occupied by that object.
Here given that originally diameter was 16 inches but then dimensions of the globe was reduced by half
The new diameter is equal to
[tex]$$D=16 / 2=8 \mathrm{in}$$[/tex]
Hence radius is equal to
[tex]$$r=8 / 2=4 \mathrm{in}$$[/tex]
The volume of the reduced globe is
[tex]$V=\frac{4}{3}(\pi)(r)^{3}$[/tex]
[tex]$V=\frac{4}{3}(3.14)(4)^{3}$\\[/tex]
[tex]$V= 267.9 \text{ in}^{3}$[/tex]
If dimensions of the globe that is 16 inches in diameter were reduced by half, then its volume would be [tex]$V= 267.9 \text{ in}^{3}$[/tex]
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Answer:
267.9 in3
Step-by-step explanation:
I took the test and got it right!
Convert 42 to a base two
numeral
Answers
numeral
Answer- 101010
Which sentence is Correct and please take your time !!!
Answers
Answer:
b
Step-by-step explanation:
Answer:
The answer is the Last one
if the diameter of a circle is 124 centimeters, then what is the radius.
Answers
Answer:
radius = 62 cm
Step-by-step explanation:
radius = diameter/2
radius = 124/2 = 62 cm
Answer:
the radius 62
Step-by-step explanation:
the radius is really just the diameter split in half.
So, 124/2 = 62
Which expression is the result of factoring the expression below by taking out its greatest common factor? 16x^2-8x=? Choose 1 answer: A. 8(2x-1) B. 8(2x^2-x) C. 8x(2x-1) D.8x(2x^2-x)
Answers
Answer:
I think it is A
Step-by-step explanation:
I NEED HELPPP ASAP pleaseeeeeee
Answers
Answer:
Subtract 23 from both sides
Step-by-step explanation:
This is how algebra works, to get a variable by itself you have to do the opposite to both sides. Hope this helped.
Answer:
It's D: subtract 23 from both sides of the equation because inverse operations
Step-by-step explanation:
Find the slope of the line
Answers
Answer:
-5/4 is the slope of the line.
which fraction correctly represents 0.54
Answers
Answer:
27/50 is the fraction.
Step-by-step explanation:
please HELP! USE PYTHAGOREAN THEOREM TO FIND RIGHT TRIANGLE SIDE LENGTHS
formula A(2)+B(2)=C(2)
Answers
Answer:
x = √ 40
Step-by-step explanation:
6 x 6 = 36 2 x 2 = 4 36 + 4 = 40Find the answer
A.
B.
C.
Answers
I use the formula A= bh/2 it’s the same thing
8x17 = 136
136/2 = 68
this is another question we cant figure out this is like multiple answers to it so yea pls help.
Answers
do it in your own answer