Select the type of equations.
consistent
equivalent
inconsistent
Arrange the summation expressions in increasing order of their values.
∑ 4 * 5^(i-1) = 4 + 20 + 100 + 500 = 624
∑ 3 * 4^(i-1) = 3 + 12 + 48 + 192 + 768 = 1,023
∑ 5* 6^(i-1) = 5 + 30 = 35
∑ 5^(i-1) = 1 + 5 + 25 + 125 = 156
Answer:
∑ (i=1, 2) 5 * 6^(i-1) < ∑ (i=1, 4) 5^(i-1) < ∑ (i=1, 4) 4 * 5^(i-1) <
< ∑ (i=1, 5) 3 * 4^(i-1)
A delivery truck is transporting boxes of two sizes: large and small. the combined weight of a large box and a small box is 95 pounds. the truck is transporting 50 large boxes and 65 small boxes. if the truck is carrying a total of 5275 pounds in boxes, how much does each type of box weigh?
Final answer:
By setting up a system of linear equations from the given conditions, we can determine that a large box weighs 60 pounds, and a small box weighs 35 pounds.
Explanation:
To solve the problem involving the weights of large and small boxes being transported by a delivery truck, we can set up a system of linear equations. Let L represent the weight of a large box and S represent the weight of a small box. We know from the problem statement the following:
A large box plus a small box weighs 95 pounds: L + S = 95
Total weight of all boxes: 50L + 65S = 5275
Now we can solve this system of equations by substitution or elimination. If we solve the first equation for L, we get L = 95 - S. Substituting this into the second equation gives us:
50(95 - S) + 65S = 5275
Expanding and simplifying the equation, we get:
4750 - 50S + 65S = 5275
15S = 5275 - 4750
15S = 525
S = 35
Now that we have the weight of the small box, we can substitute it back into the first equation to find the weight of the large box:
L + 35 = 95
L = 60
Therefore, a large box weighs 60 pounds, and a small box weighs 35 pounds.
hey I really need help its a test -3x=48
5x-1=29
4(x-6)+7=23
3(x-4)+5x=4
The formula for the area of a triangle is A = 1/2bh, where b is the length of the base and h is the height. The equation solved for h is h =2a/b The formula for the area of a triangle is A = bh, where b is the length of the base and h is the height. The equation solved for h is h = . Find the height of a triangle that has an area of 30 square units and a base measuring
12 units. 3 units 5 units 8 units 9 units
the answer is 5 units i know this because i just took a test with this question
A recipe for punch says to use 4 1/2 of lemonade for each cup of ginger ale. If you use 1 2/5 cups of ginger ale, how much lemonade should you use?
please help. i get two diff ans.
If the interest rate is 3% and a total of $4,370.91 will be paid to you at the end of 3 years, what is the present value of that sum? A) $3900, B) $3947 C) $3,977.40 D) $4000,
25 points!
Answer both! please leave explanation!
Help: Scientists think the _____ is a solid iron with a layer of liquid iron surrounding it.
1. Outer core
2. Inner core
3. Mantle
4. Crust,
Which of these denominations in no longer made in the United States?
A. $1000
B. $50
C. $2
D. $100
Answer:
$1000
Step-by-step explanation:
A person at ground level measures the angle of elevation to the top of a building to be 74°. If at this point the person is 34 feet away from the base of the building, then how tall is the building?
Please round to the tenths place.
Please show work/steps and provide units with your answer.
the leg of each isosceles right triangle when the hypotenuse is of the given measure. Given = 5sqrt6
Hi guys can you help me factor these two equations?
5x^2-13x-6
4x^4 – 28x^3 + 48x^2
please show your work on both of them, and thank you so much!
(Edit I have to repost this question bc i really need it answered. I'm offering more points now!
sav meh pl0x ty fam
Mean: 42
Median: 38
Range: 52
Mean Deviation: 11.23
Shift 1
18
25
56
42
29
38
54
47
35
30
Shift 2
23
19
50
49
67
34
30
59
40
33
Shift 3
19
22
24
40
45
29
33
29
39
59
Shift 4
21
23
25
40
35
19
70
40
22
23
The summary statistics for all of the workers at a steel factory are shown. Four sample groups were taken from each of the four shifts. For which sample group is the mean closest to the population mean?
A) Shift 1
B) Shift 2
C) Shift 3
D) Shift 4
A is an acute angle in a right triangle, Given that Sin A= 7/25, what is the ratio for Cos A? Enter your answer in the box as a fraction in simplest form.
Consider the incomplete paragraph proof. Given: Isosceles right triangle XYZ (45°–45°–90° triangle) Prove: In a 45°–45°–90° triangle, the hypotenuse is times the length of each leg. Because triangle XYZ is a right triangle, the side lengths must satisfy the Pythagorean theorem, a2 + b2 = c2, which in this isosceles triangle becomes a2 + a2 = c2. By combining like terms, 2a2 = c2. Which final step will prove that the length of the hypotenuse, c, is times the length of each leg? Substitute values for a and c into the original Pythagorean theorem equation. Divide both sides of the equation by two, then determine the principal square root of both sides of the equation. Determine the principal square root of both sides of the equation. Divide both sides of the equation by 2.
Answer:
Step-by-step explanation:
In a 45°–45°–90° triangle, the hypotenuse is times the length of each leg. Because triangle XYZ is a right triangle, the side lengths must satisfy the Pythagorean theorem that is:
[tex]a^{2}+b^{2}=c^{2}[/tex], which in this isosceles triangle becomes [tex]a^{2}+a^{2}=c^{2}[/tex] as a=b in isosceles triangle.
By combining the like terms, [tex]2a^{2}=c^{2}[/tex]
Now, we will determine the principal square root of both sides of the equation,
[tex]c=\sqrt{2}a[/tex] (since a is positive)
Divide both sides of the equation by 2, we get
[tex]\frac{c}{2}=\frac{\sqrt{2}a}{2}[/tex]
[tex]\frac{c}{2}=\frac{a}{\sqrt{2}}[/tex]
[tex]c=\frac{2a}{\sqrt{2}}[/tex]
[tex]c=\sqrt{2}a[/tex]
Now, as a=b, then [tex]c=\sqrt{2}b[/tex]
Find the number of sides of a regular polygon if the interior angle is 150
Find the area of a parallelogram with a height 15 cm and a base of 18 and 2/3 cm
1. Given a || b , c || d, and . Find the measure of angles 1 through 12 in the complex figure.
In summary:
- Angle 1 = Angle 2 = Angle 3 = Angle 4 = 69°
- Angle 5 = Angle 6 = Angle 7 = Angle 8 = 116°
- Angle 9 = Angle 10 = 69°
- Angle 11 = Angle 12 = 116°
Let's analyze the complex figure with parallel lines and transversals. We have two parallel lines, a and b, intersected by two transversals. I'll break down the problem step by step:
1. Angle 1: This angle is formed by the intersection of a and the transversal. It is an **alternate interior angle** with the angle measuring 69°. Therefore, **Angle 1 = 69°**.
2. **Angle 2**: It is also an alternate interior angle with the same measure as **Angle 1**. Hence, **Angle 2 = 69°**.
3. **Angle 3**: This angle is formed by the intersection of **b** and the transversal. It is a **corresponding angle** to **Angle 1**. Therefore, **Angle 3 = 69°**.
4. **Angle 4**: It is a corresponding angle to **Angle 2**. Thus, **Angle 4 = 69°**.
5. **Angle 5**: This angle is formed by the intersection of **c** and the transversal. It is an **alternate interior angle** with the angle measuring **116°**¹. Therefore, **Angle 5 = 116°**.
6. **Angle 6**: It is also an alternate interior angle with the same measure as **Angle 5**. Hence, **Angle 6 = 116°**.
7. **Angle 7**: This angle is formed by the intersection of **d** and the transversal. It is a **corresponding angle** to **Angle 5**. Therefore, **Angle 7 = 116°**.
8. Angle 8: It is a corresponding angle to Angle 6. Thus, Angle 8 = 116°.
9. Angle 9: It is a vertical angle to Angle 1. Therefore Angle 9 = 69°.
10. Angle 10: It is a vertical angle to Angle 2. Thus Angle 10 = 69°.
11. Angle 11: It is a vertical angle to Angle 5. Therefore, Angle 11 = 116°.
12. Angle 12: It is a vertical angle to Angle 6. Thus, Angle 12 = 116°.
Find the volume of a cylinder with a radius of 5 cm and a height of 10 cm. Then, find the volume of the cylinder if the radius is increased to 10 cm. Leave your answers in term of pi.
Volume of cylinder is 250πcm³ and volume of the new cylinder is 1000πcm³.
How to determine the volume of the cylinder?The volume of the cylinder can be determined by multiplying area of base with height of the cylinder.
V=πr²*h
where r is the radius of base of the cylinder and h is the height of the cylinder.
following this above formula in given problem,
radius of the base of the cylinder= 5cm
height of the cylinder=10cm
volume= V=πr²*h= π5²*10= 250π cm³
Now the radius of the cylinder is increased to 10cm.
now r=10cm
height of the cylinder=10cm
volume= V=πr²*h= π10²*10= 1000π cm³
Therefore volume of cylinder is 250πcm³ and volume of the new cylinder is 1000πcm³.
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(-6)^-12(-6)^5(-6)^2
What is the area of a regular hexagon with a side length of 4 m? Enter your answer in the box. Round only your final answer to the nearest hundredth.
The area of a regular hexagon with a side of 4m is 24√3.
Side of the regular hexagon = 4m
What is a regular hexagon?A Regular hexagon is a polygon with 6 equal sides.
We know that a regular hexagon with a side p comprises 6 equilateral triangles with a side p.
So, the area of a regular hexagon with side p= area of 6 equilateral triangles with side p.
So, the area of a regular hexagon with side p = [tex]6*\frac{\sqrt{3} }{4} p^{2}[/tex]
The area of a regular hexagon with a side of 4m = [tex]6*\frac{\sqrt{3} }{4} 4^{2}[/tex]
The area of a regular hexagon with a side of 4m =24√3.
Therefore, The area of a regular hexagon with a side of 4m is 24√3.
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Colinda has just purchased her first home for $125,000. She put down a 20 percent down payment of $25,000 and took out a 4 percent mortgage for the rest. Her mortgage payment is $477 per month. How much of her first monthly mortgage payment is amortization?
Colinda's first monthly mortgage payment includes $143.70 towards amortization, after subtracting the first month's interest of $333.30 from the total payment of $477.
Explanation:To determine how much of Colinda’s first monthly mortgage payment is for amortization, we must first calculate the amount of her payment that goes towards interest and then subtract this from the total monthly payment.
Colinda bought a house for $125,000, made a 20% down payment ($25,000), and took out a mortgage for the remaining $100,000 at a 4% annual interest rate. Her monthly mortgage payment is $477.
First, calculate the monthly interest rate: 4% annually means 0.04 / 12 per month = 0.003333. Therefore, the first month’s interest on the mortgage is $100,000 * 0.003333 = $333.30.
Next, subtract the interest from the total monthly payment to find the amortization portion: $477 (total monthly payment) – $333.30 (interest) = $143.70 towards amortization.
The amount of Colinda's first monthly mortgage payment that is amortization is approximately $143.67.
To separate the interest portion from the total payment.
First, let's calculate the monthly interest rate:
[tex]\text{Monthly interest rate} = \frac{4 \%}{12} = \frac{0.04}{12} = 0.00333 \text{ (approx.)}[/tex]
Next, we calculate the interest portion of the first payment:
[tex]\text{Interest portion} = \text{Principal} \times \text{Monthly interest rate}[/tex]
[tex]\text{Interest portion} = 100,000 \times 0.00333 = 333.33 \text{ (approx.)}[/tex]
Now, to find the amortization portion, we subtract the interest portion from the total monthly payment:
[tex]\text{Amortization portion} = \text{Total monthly payment} - \text{Interest portion}[/tex]
[tex]\text{Amortization portion} = 477 - 333.33 = 143.67[/tex]
What was the original price if:
a
after increasing by 30% it became $520?
Answer:
Original price was $400.
Step-by-step explanation:
Let the original price = x dollars.
It is given that the new price is obtained by increasing the original price by 30% i.e. 0.3
As, the new price is $520.
So, we have the relation,
[tex]x+0.03x=520[/tex]
i.e. [tex]1.3x=520[/tex]
i.e. [tex]x=\frac{520}{1.3}[/tex]
i.e. x = 400
Hence, the original price was $400.
This is really confusing... making my head hurt. I don't understand it AT ALL. If I get this one wrong, and all the other three like this, I'm gonna fail my test.
Can you figure out number 8 please and show how you got it?
You're working with a geometric problem where the probability of success is constant in each trial. This is related to the situation where you repeatedly ask students if they live within a five-mile radius. The problems you've mentioned seem to involve figuring out specifics related to degrees and interpreting figures.
Explanation:It sounds like you're dealing with a geometric problem. Geometric problems often involve situations where the probability of success or failure stays constant across trials. For example, you inquire if a person lives within five miles of you - the probability is fixed, regardless of the number of people you ask.
Let's decipher it step by step. Firstly, visualize each instance (trial) as the asking of a question to a student and consider success as the event where the student lives within five miles. Probability of success then stays the same every time you ask.
In problem 91, it's important to understand the degrees involved. The first part mentions 88.6°. Without the full problem, it's hard to give a direct answer here, but angles often play a part in geometry and trigonometry problems, it could be related to that. As for the figures mentioned (Car X, the hash marks) they would likely be visible on a diagram accompanying your problem and would inform the solution.
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barb is making a bead necklace. she strings 1 white bead, then 3 blue beaads, then 1 white bead, and so on. write the numbers for the first eight beads that are white. what is a rule for the pattern.,
What is the volume of a cylinder with base radius 3 and height 8?
Answer is provided in the image attached.
Final answer:
The volume of a cylinder with a base radius of 3 and a height of 8 is approximately 226.195 cubic units, using the formula V = πr²h.
Explanation:
The volume of a cylinder is calculated using the formula V = πr²h, where π is the constant pi (approximately 3.14159), r is the radius of the cylinder's base, and h is the height of the cylinder. For a cylinder with base radius 3 and height 8, we use the values directly in the formula:
V = π×(3²)×8
V = π×9×8
V = π×72
V = 3.14159×72
V ≈ 226.195 cubic units
Therefore, the volume of the cylinder is approximately 226.195 cubic units.
A certain drug is made from only two ingredients: compound a and compound
b. there are 7 milliliters of compound a used for every 4 milliliters of compound
b. if a chemist wants to make 748 milliliters of the drug, how many milliliters of compound b are needed?
Jack just opened a checking account at the bank. Within the first month, he deposited three checks for $34.98, $51.02, and $51.22. He withdrew $3.23 for new pencils, $4.22 for cards, and $9.79 for movies from his account in the same month.
Order the rational numbers from least to greatest and explain your reasoning.
At the beginning of the month Jack’s balance was $98. What was his balance at the end of the
month after all of his deposits and withdrawals? Show your work, no credit will be given for just an
answer.
what is the product? (9t-4)(-9-4)
Answer: The product of [tex](9t-4)(-9-4)[/tex] is -117t+52.
Explanation:
The given expression is,
[tex](9t-4)(-9-4)[/tex]
Simplify the above expression.
[tex](9t-4)(-13)[/tex]
Use distributive property t simplify the above expression.
[tex](9t-4)(-13)=9t\times (-13)-4\times(-13)[/tex]
[tex](9t-4)(-13)=117t+52[/tex]
Therefore, the product of [tex](9t-4)(-9-4)[/tex] is -117t+52.