On which triangle can the law of cosines be used to find the length of an unknown side?

Law of cosines: a2 = b2 + c2 – 2bccos(A)

Triangle Q R S is shown. The length of Q R is s, the length of R S is q, and the length of Q S is 12. Angle R Q S is 36 degrees, angle Q S R is 57 degrees, and angle S R Q is 87 degrees.
Triangle Q R S is shown. The length of Q R is s, the length of R S is 7, and the length of Q S is 12. Angle R S Q is 57 degrees.
Triangle Q R S is shown. The length of Q R is s, the length of R S is 7, and the length of Q S is b. Angle R S Q is 57 degrees and angle S Q R is 36 degrees.
Triangle Q R S is shown. The length of Q R is s, the length of R S is q, and the length of Q S is 12. Angle R Q S is 36 degrees and angle Q S R is 57 degrees.

The correct dotplot for the given data is option D, which displays the number of errors for the week for each workstation.

Error in math is any mistake made in the process of solving a mathematical problem or problem-solving process. It could mean a mistake in the calculations, incorrect steps taken, or incorrect assumptions made. It can also include making a wrong interpretation of the problem, or not being able to solve it at all. Errors in math can occur due to a lack of understanding of the concepts, mistakes in calculations, errors in reasoning, or incorrect application of the rules and formulas. Errors can also be made in the process of writing down the equations, or in the process of simplifying the equation.

The graph begins with 0 and goes up to 254201 in intervals of 5. The data points for each work station are marked on the graph, showing the number of errors each work station made. This visual display of data points allows for an easy comparison of the number of errors across all workstations.

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The n-intercept of the function n(t) = 8 * 2log₃(t+1) is (0, 8), and the t-intercept is (-1, 0). The n-intercept represents the point where the function intersects the y-axis, and in this case, it means that when t is zero, the value of n is 8. The t-intercept represents the point where the function intersects the x-axis, and in this case, it means that when n is zero, the value of t is -1.

To find the n-intercept, we set t = 0 and evaluate the function:

n(0) = 8 * 2log₃(0+1)

= 8 * 2log₃(1)

= 8 * 2 * 0

= 0

Therefore, the n-intercept is (0, 8), meaning that when t is zero, the value of n is 8.

To find the t-intercept, we set n = 0 and solve for t:

0 = 8 * 2log₃(t+1)

Since log₃(t+1) is always positive, the only way for the product to be zero is if the coefficient 8 * 2 is zero. However, since 8 * 2 ≠ 0, there are no real solutions for t that make n zero.

Hence, there is no t-intercept for this function.

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The solution for the given equation is C) \(x=\frac{-1+-\sqrt{33} }{4}\)

What does a quadratic function mean?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other words, a "polynomial function of degree 2" is a quadratic function.

The formula for the solution of a quadratic equation \(ax^{2} +bx+c=0\) is

\(x=\frac{-b+-\sqrt[2]{b^{2}-4ac } }{2a}\).

So, the solution for the equation \(2x^{2} +x-4=0\) is

\(x=\frac{-1+-\sqrt[2]{1^{2}-4*2*(-4) } }{2*2}\\x=\frac{-1+-\sqrt[2]{1+32 } }{4}\\x=\frac{-1+-\sqrt{33} }{4}\)

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Answer:

C I think

Step-by-step explanation:

The probability that a random point on the line segment AK will be on the line segment CD is 0.6 or 60%.

To calculate the probability that a random point on the line segment AK will be on the line segment CD, we need to compare the lengths of the line segments CD and AK.

Let's start by finding the length of line segment AK. We can see that AK spans from point A to point K, which covers 5 units on the x-axis.

Next, let's find the length of line segment CD. We can see that CD spans from point C to point D, which covers 3 units on the x-axis.

Since the length of line segment AK is 5 units and the length of line segment CD is 3 units, the probability that a random point on AK will be on CD is given by the ratio of the lengths:

P = (Length of CD) / (Length of AK) = 3 / 5 = 0.6

Therefore, the probability that a random point on the line segment AK will be on the line segment CD is 0.6 or 60%.

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Answer:

\(A(t) = \pi (0.5 + 2t)^2\)

Step-by-step explanation:

Given

\(r(t) = 0.5 + 2t\)

\(A(r) = \pi r^2\)

Required

Determine composite function to find A in terms of t

The interpretation of this question is to determine A(t) and this is solved as follows:

Because:

\(r(t) = 0.5 + 2t\)

And we want to eliminate r in \(A(r) = \pi r^2\)

We have to substitute 0.5 + 2t for r in \(A(r) = \pi r^2\)

\(A(r) = \pi r^2\)  becomes

\(A(t) = \pi (0.5 + 2t)^2\)

The solution can be solved further, but it is best left in this form:

\(A(t) = \pi (0.5 + 2t)^2\)

The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)).

Let the functions be f(x) = 4x² + 1 and g(x) = x² - 3

The correct answer is (f o g)(x) = 4x⁴ - 96x + 37 and

(g o f)(x) = 16x⁴ + 8x² - 2.

The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)). In this operation, the function g exists used for the outcome of applying the function f to x.

Given:

f(x) = 4x² + 1 and g(x) = x² - 3

a) (f o g)(x) = f[g(x)]

f[g(x)] = 4(x² - 3)² + 1

substitute the value of g(x) in the above equation, and we get

    = 4(x⁴ - 24x + 9) + 1

simplifying the above equation

    = 4x⁴ - 96x + 36 + 1

    = 4x⁴ - 96x + 37

(f o g)(x) = 4x⁴ - 96x + 37

b) (g o f)(x) = g[f(x)]

substitute the value of g(x) in the above equation, and we get

g[f(x)] = (4x² + 1)²- 3

      = 16x⁴ + 8x² + 1 - 3

simplifying the above equation

      = 16x⁴ + 8x² - 2

(g o f)(x) = 16x⁴ + 8x² - 2.

Therefore, the correct answer is (f o g)(x) = 4x⁴ - 96x + 37 and

(g o f)(x) = 16x⁴ + 8x² - 2.

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Answer:

I think its about 9? being as if you look a it its close to 12 but nowhere near it.

The new height of the tsunami wave is 0.93 times the height before R is increased by 1.5.

(a) Calculation of height of tsunami wave in 20 feet deep water, given that its height is 7 feet at the origin (in water 20,000 feet deep) is as follows:

First, we need to calculate the ratio of the depth of water at origin to the depth of water at the given location.

The ratio is R = D/dR

= 20000 / 20R

= 1000

The new height of the tsunami wave h is given by

h = HR0.25h

= 7 x (1000)0.25h

= 7 x 5.62h

= 39.34 feet

Therefore, the height of a tsunami wave in water 20 feet deep is 39.34 feet. (rounded to two decimal places)

(b) Given that the depth ratio R is increased by 1.5 when water depth is decreased by a third. The new height of a tsunami wave is x times the height before R is increased by 1.5 is to be determined.The formula to find the new height is:

h = HR0.25

The depth ratio R is increased by 1.5, which means that the new value of R is R + 1.5h = H(R+1.5)0.25

Hence, the new height of the tsunami wave is x times the height before R is increased by 1.5 is given by

x = h / h'

where h is the original height and h' is the new height.

From the above formula, h' = H(R+1.5)0.25

Therefore, x = h / [H(R+1.5)0.25]

Substitute the given values to calculate x.

We know that H = 7, R = 1000 and the new value of R is

R + 1.5 = 1001.5x

= 7 / [7(1001.5)0.25]x

= 0.93

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a). The height of the tsunami wave in water 20 feet deep is approximately 40.68 feet.

b). The new height of the tsunami wave, h₂, is x times the height before R is increased by 1.5, where \(x = (R + 1.5)^{0.25}\).

(a) To calculate the height of a tsunami wave in water 20 feet deep if its height is 7 feet at its point of origin in water 20,000 feet deep, we need to find the water depth ratio R and then use it in the formula

\(h=H*R^{0.25}\)

Given:

H = 7 feet (height at the point of origin)

D = 20,000 feet (ocean depth)

d = 20 feet (water depth)

We can calculate the water depth ratio R using R = D/d:

R = 20,000 feet / 20 feet

R = 1000

Now, substitute the values of H and R into the formula to find the new height h:

h = 7 feet * 1000^0.25

Using a calculator or mathematical software to evaluate the expression:

h ≈ 40.68 feet

Therefore, the height of the tsunami wave in water 20 feet deep is approximately 40.68 feet.

(b) If the water depth decreases by a third, the depth ratio R is increased by 1.5.

We need to determine how this change in R affects the height of the tsunami wave.

Let's say the height of the tsunami wave before the change in R is denoted as H₁, and the new height after the change is denoted as H₂.

We have the relationship: H₂ = x * H₁,

where x is the factor by which the height is affected.

Given that the depth ratio R increases by 1.5, we can write the new depth ratio R₂ as:

R₂ = R + 1.5

We can express R₂ in terms of the original depth ratio R as:

R₂ = R + 1.5

= (D/d) + 1.5

From Green's law, we know that \(h_2 = H_2 * R_2^{0.25}\).

Substituting H₂ = x * H₁ and

R₂ = R + 1.5, we get:

\(h_2 = (x * H_1) * (R + 1.5)^{0.25\)

To find the relationship between the new height h₂ and the original height H₁, we can divide both sides of the equation by H₁:

\(h_2 / H_1 = x * (R + 1.5)^{0.25\)

Therefore, the new height of the tsunami wave, h₂, is x times the height before R is increased by 1.5, where \(x = (R + 1.5)^{0.25}\).

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Answer:

Step-by-step explanation:

There are 20 scores.

The median is 92 and first quartile is at 82 and below.

So, 88 is in 2nd quartile.

Answer:

the total amount received by him is £330

Step-by-step explanation:

The computation of the total amount of money that he received is shown below:

For 35 hours, he earns = 35 ×£8 per hour = £280

For extra 5 hours, he earns = 5 × (£8 × 1.25) = £50

Hence, the total amount received by him is £330

Answer:

14:250 15:2800

Step-by-step explanation:

14: 32%=80 dividing both sides by 8 we get 4% = 10. multiply both sides by 25 and we get 100%=250

15: same strategy, 2%=56 so 1%=28. multiply by 100 to get 100%=2800

Answer: A) 4.8 CM

Step-by-step explanation:

Answer:

b=49

Step-by-step explanation:

27+b=76

76-27= 49

b=49

Step-by-step explanation:

\( = 2 \frac{3}{7} - 5 \frac{6}{7} \\ \)

\( = \frac{2 \times 7 + 3}{7} - \frac{5 \times 7 + 6}{7} \\ \)

\( = \frac{17}{7} - \frac{41}{7} \\ \)

\( = \frac{17 - 41}{7} \\ \)

\( = \frac{ - 24}{ \: 7} \\ \)

☘☘☘...

Answer:

a) 52

b) 21 + 6.25π

Step-by-step explanation:

Part (a)

the sides which we don't have:

(longer side): 7+6 = 13m

(shorter side): 13—8= 5m

So:

Perimeter = 2P = 13+5+7+8+6+13=52

Part (b)

perimeter of the half circle:

\(\pi \times {r}^{2} = \pi \times {2.5}^{2} = 6.25\pi\)

So:

Perimeter = 2P = 2×8 + 5 + 6.25π = 21 + 6.25π

Answer:

c. 9 units

Step-by-step explanation:

the total amount of oil that leaks out over the entire time interval [0, 120].

integral ∫₀¹₂₀ r(t) dt represents the total amount of oil that leaks from the tank in 120 minutes.

To see why, consider the definition of an integral. If we divide the interval [0, 120] into small subintervals of width Δt, then the amount of oil that leaks out during each subinterval is approximately r(t)Δt. Summing up all these small amounts over the entire interval gives:

Σᵢ r(tᵢ) Δt

where tᵢ is the midpoint of the i-th subinterval. As we take the limit as the subinterval width goes to zero, this sum becomes the integral:

∫₀¹₂₀ r(t) dt

which represents the total amount of oil that leaks out over the entire time interval [0, 120].

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Answer:

2.8 or 2 4/5

Step-by-step explanation:

Here's our proportion of cups of milk to servings

3 1/2:10      For my sake I'm using decimals

3.5:10

Now let's try to get our servings to 1 (a unit rate)

0.35:1         I divided by 10 on each side

We need 8 servings not 1 so let's multiply 8 on each side

2.8:8

In case you want it in fraction form we can do 2 8/10 and simplify it to 4/5 by dividing by 2. Our answer is 2.8 or 2 4/5 cups of milk for 8 servings.

Answer:

3g

Step-by-step explanation:

Answer:

56.25%

Step-by-step explanation:

The spinner had the numbers 1, 3, 5, and 6.

3/4 * 3/4 = 9/16

9/16 = 0.6525 = 56.25%

The  probability of spinning the spinner and the arrow landing on an odd number is 25/81.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

The spinner have markings {1, 2, 3, 4, 5, 6, 7, 8, 9}

So, the probability of spinning the spinner and the arrow landing on an odd number is 5/9

and, again the probability of spinning the spinner and the arrow landing on an odd number second time

= 5/9 x 5/9

= 25/ 81

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Answer:

1.063

Step-by-step explanation:

Firstly, I turned the grams to kg=0.209

then i subtracted the full bottle's weight with the empty bottle.

First you graph "y = 2x +2." You shade in the region below it, because it's y "LESS THAN" and you keep the line solid (not dotted) because it's "equal to" 2x+2 too.

The probability that Tamika's result is greater than Carlos' result is $\boxed{\frac{4}{9}}$.

To solve this problem, we can start by finding all the possible sums that Tamika can get by adding two different numbers from the set $\{8,9,10\}$:

- $8+9=17$
- $8+10=18$
- $9+10=19$

Similarly, we can find all the possible products that Carlos can get by multiplying two different numbers from the set $\{3,5,6\}$:

- $3\times5=15$
- $3\times6=18$
- $5\times6=30$

Now we need to compare each sum with each product to see which ones satisfy the condition that Tamika's result is greater than Carlos' result. We can organize this information in a table:

| Tamika's sum | Carlos' product | Tamika's sum > Carlos' product? |
| ------------ | -------------- | ----------------------------- |
| 17           | 15             | Yes                           |
| 17           | 18             | No                            |
| 17           | 30             | No                            |
| 18           | 15             | Yes                           |
| 18           | 18             | No                            |
| 18           | 30             | No                            |
| 19           | 15             | Yes                           |
| 19           | 18             | Yes                           |
| 19           | 30             | No                            |

Out of the 9 possible combinations, there are 4 that satisfy the condition, namely when Tamika gets a sum of 17, 18 (twice), or 19 and Carlos gets a product of 15 or 18. Therefore, the probability that Tamika's result is greater than Carlos' result is $\boxed{\frac{4}{9}}$.

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Answer:

\(x^\frac{9}{5}\)

Step-by-step explanation:

\(\sqrt[5]{x}\) is the same thing as \(x^{\frac{1}{5}}\).

Now if we have \(x^{\frac{1}{5}}\) to the power of 9, the exponents are multiplied.

\(x^{\frac{1}{5} \cdot9} = x^{\frac{9}{5} }\).

Hope this helped!

Answer:

2

Step-by-step explanation:

All u need to do, is subtract 3, until u get to the 20th sequence.

59, 56, 53, 50, 47, 44, 41, 38, 35, 32, 29, 26, 23, 20, 17, 14, 11, 8, 5, 2