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FrozenT
13 days ago
15

Find the distance across the lake. Assume the triangles are similar.

Mathematics
1 answer:
Zina [3.8K]13 days ago
5 0

Response:

B. 255 m

Detailed breakdown:

utilize similar triangles

L / 60 = 85 / 20

L = (85 * 60) / 20

L = 255 m

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Suppose the coordinate of a is 0, ar = 5, and at =7. What are the possible coordinates of the midpoint of rt ?
Zina [3893]

Here, 'a' relates to 0.

There are two scenarios for 'r' and 't'.

Scenario 1.

Both are positioned on the same side to the right of 'a'.

In this case, 'r' would equal 5, and 't' would equal 7.

The midpoint between 'r' and 't' is \frac{5+7}{2} =6.

Scenario 2.

If both are found to the left of 'a'.

Then 'r' would equal -5, while 't' would equal -7.

The midpoint is \frac{-7-5}{2} =-6.

Scenario 3.

If 'r' is right of 'a' and 't' is left of 'a'.

Thus 'r' equals 5 and 't' equals -7.

The midpoint is \frac{-7+5}{2}=-1.

Scenario 4.

If 'r' is left of 'a' while 't' is right of 'a'.

In this case, 'r' corresponds to -5 and 't' corresponds to 7.

The midpoint is \frac{-5+7}{2}=1.

The potential midpoint coordinates for 'rt' are 6, -6, 1, and -1.

4 0
1 day ago
Initially 5 grams of salt are dissolved into 10 liters of water. Brine with concentration of salt 5 grams per liter is added at
Svet_ta [4296]

The salt enters at a rate of (5 g/L)*(3 L/min) = 15 g/min.

The salt exits at a rate of (x/10 g/L)*(3 L/min) = 3x/10 g/min.

Thus, the total rate of salt flow, represented by x(t) in grams, is defined by the differential equation,

x'(t)=15-\dfrac{3x(t)}{10}

which is linear. Shift the x term to the right side, then multiply both sides by e^{3t/10}:

e^{3t/10}x'+\dfrac{3e^{t/10}}{10}x=15e^{3t/10}

\implies\left(e^{3t/10}x\right)'=15e^{3t/10}

Next, integrate both sides and solve for x:

e^{3t/10}x=50e^{3t/10}+C

\implies x(t)=50+Ce^{-3t/10}

Initially, the tank contains 5 g of salt at time t=0, so we have

5=50+C\implies C=-45

\implies\boxed{x(t)=50-45e^{-3t/10}}

The duration required for the tank to contain 20 g of salt is t, such that

20=50-45e^{-3t/10}\implies t=\dfrac{20}3\ln\dfrac32\approx2.7031\,\mathrm{min}

3 0
8 days ago
An ANOVA procedure is applied to data obtained from 6 samples where each sample contains 20 observations. The degrees of freedom
PIT_PIT [3895]

Answer:

C. 5 degrees of freedom for the numerator and 114 for the denominator

Step-by-step explanation:

Analysis of variance (ANOVA) is utilized to examine the variations among group means within a sample.

The sum of squares represents the cumulative square of variation, which refers to the deviation of each individual value from the grand mean.

Assuming there are 6 groups and each group contains j=1,\dots,20 individuals, the variation can be calculated using the following formulas:

SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2

SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2

SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2

This also has the property

SST=SS_{between}+SS_{within}

The numerator's degrees of freedom in this case is given by df_{num}=df_{within}=k-1=6-1=5 where k = 6 represents the number of groups.

The denominator's degrees of freedom in this scenario is indicated by df_{den}=df_{between}=N-K=6*20-6=114.

The total degrees of freedom would be df=N-1=6*20 -1 =119.

Thus, the appropriate answer would be 5 degrees of freedom for the numerator and 119 degrees of freedom for the denominator.

C. 5 numerator and 114 denominator degrees of freedom

8 0
2 days ago
The Freeman family is barbecuing veggie burgers, corn cobs, and mushroom caps in their local park. If 3/8 of the items barbecued
AnnZ [3868]

Answer:

7/24

Step-by-step explanation:

All the items being grilled collectively equal 1.

Each item represents a fractional portion of 1.

Combine 3/8 and 1/3, then subtract that sum from 1.

3/8 + 1/3 = 9/24 + 8/24 = 17/24

This means that veggie burgers and corn contribute to 17/24 of the total.

To determine the fraction accounted for by mushrooms, we take 1 and subtract 17/24.

1 - 17/24 = 24/24 - 17/24 = 7/24.

Final answer: 7/24

8 0
11 days ago
Which statement is true about the polynomial 3j4k−2jk3+jk3−2j4k+jk3 after it has been fully simplified? in terms and degree
zzz [4002]

I just took this assessment and got it right; the answer is a term with a degree of 5. It’s option 4.

7 0
6 hours ago
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