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17 days ago

What is the approximate angle measure for angle W in the triangle below?

Mathematics

1 answer:

lawyer [9.2K]17 days ago

3 0

Given that we have all three sides of the triangle, we can classify this as a Side-Side-Side (SSS) triangle. To find the angle, we start by applying the Law of Cosines specifically to the side opposite the angle of interest, which is angle W, opposite side XV:
XV² = XW² + WV² - 2(XW)(WV)cos W
Plugging in the known values:
116² = 96² + 89² - 2(96)(89)cos W
Calculating W
13,456 = 9,216 + 7,921 - 17,088 cos W
13,456 = 17,137 - 17,088 cos W
13,456 - 17,137 = 17,137 - 17,088 cos W - 17,137
-3,681 = -17,088 cos W
(-3,681)/(-17,088) = (-17,088 cos W)/(-17,088)
0.215414326 = cos W
cos W = 0.215414326

To find W:
W = cos^(-1)(0.215414326)
Calculating with a calculator:
W ≈ 77.56016397°
Rounded to one decimal place:
W ≈ 77.6°

Answer: The third option, 77.6°

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What is a31 of the arithmetic sequence for which a5=12.4 and a9=22.4

PIT_PIT [9159]

In an arithmetic sequence
a₁, a₂, a₃,...,
the n-th term is
$a_{n}=a_{1}+(n-1)d$
where d = the common difference

Given that a₅ = 12.4,
a₁ + 4d = 12.4 (1)
With a₉ = 22.4,
a₁ + 8d = 22.4 (2)

Subtracting (1) from (2) yields:
a₁ + 8d - (a₁ + 4d) = 22.4 - 12.4
4d = 10
Thus, d = 2.5
From (1),
a₁ = 12.4 - 4*2.5 = 2.4

Consequently,
a₃₁ = 2.4 + 30*2.5 = 77.4
Answer: a₃₁ = 77.4

6 0

9 days ago

J.J.Bean sells a wide variety of outdoor equipment and clothing. The company sells both through mail order and via the internet.

babunello [8443]

The 99% confidence interval for the actual mean difference between average mail-order and internet purchase amounts falls within [$(-31.82), $12.02].

Step-by-step clarification:

We know a random sample of 16 mail-order sales receipts shows a mean sale amount of $74.50 and a standard deviation of $17.25.

For internet sales, a random sample of 9 receipts gives a mean sale amount of $84.40 with a standard deviation of $21.25.

The pivotal value utilized for constructing a 99% confidence interval for the true mean difference is given by;

P.Q. =

where,

= sample mean of mail-order sales = $74.50 $\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }$ $t__n_1_+_n_2_-_2$

= sample mean of internet sales = $84.40

$\bar X_1$ = standard deviation for mail-order sales = $17.25

$\bar X_2$ = standard deviation for internet sales = $21.25

$s_1$ = number of mail-order sales receipts = 16

= number of internet sales receipts = 9 $s_2$

Furthermore,

= $n_1$ = 18.74

$n_2$

The actual mean difference between average mail-order and internet purchases is denoted by ( $s_p =\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }$ $\sqrt{\frac{(16-1)\times 17.25^{2}+(9-1)\times 21.25^{2} }{16+9-2} }$

Thus, the 99% confidence interval for ( $\mu_1-\mu_2$ ) is expressed as;

= $\mu_1-\mu_2$ Here, the t critical value at the 0.5% significance level with 23 degrees of freedom is 2.807. =

= [$-31.82, $12.02] $(\bar X_1-\bar X_2) \pm t_(_\frac{\alpha}{2}_) \times s_p \times \sqrt{\frac{1}{n_1} +\frac{1}{n_2}}$

Therefore, the 99% confidence interval for the true mean difference between average mail-order and internet purchases is [$(-31.82), $12.02].

$(74.50-84.40) \pm (2.807 \times 18.74 \times \sqrt{\frac{1}{16} +\frac{1}{9}})$

5 0

15 days ago

Please help ASAP Payton collected data to show the relationship between the number of hours he practices and the number of error

lawyer [9256]

Response:

Option B.

Step-by-step breakdown:

The general equation for the best fit line is

$y=ax+b$

where a indicates the slope and b the y-intercept.

Utilizing a graphing calculator yields a=-4.54762 and b=43.7143. Hence, the equation for the best fit line can be represented as

$y=-4.54762x+43.7143$

Here,

$Slope=-4.54762$

$Slope\approx -4.5$

Note: Alternatively, you can apply the following formula to compute the slope.

$m=\dfrac{\overline{x}\cdot \overline{y}-\overline{xy}}{(\overline{x})^2-\overline{x^2}}$

Accordingly, the correct choice is B.

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2 days ago

When Margo makes cheese ravioli, she uses both ricotta and mozzarella cheeses to make the filling. She often varies the proporti

Zina [9184]

Answer:

cuando hables de raviolis de queso, dile a Martha que vaya al supermercado a comprar raviolis Chef Boyardee.

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29 days ago

Determine the input value for which the statement f(x) = g(x) is true. From the graph, the input value is approximately_______ .

babunello [8443]

For this inquiry, we are presented with a graph, and we're tasked with determining the x-coordinate of where the two lines intersect.

An examination of the graph indicates that the input value is around 3.3.

In the graph,

$f(x) =3$

To derive g(x), we need the slope and y-intercept.

The slope represents the ratio of vertical change to horizontal change.

In this case, the rise is 3 units and the run is 2 units. The line intersects the y-axis at -2.

Thus, the equation for g(x) becomes

$g(x) = \frac{3}{2}x -2$

Next, we will perform

$f(x)= g(x)$

Substituting the values of both functions will yield

$3 = \frac{3}{2}x -2$

By adding 2 to both sides, we have

$5 = \frac{3}{2}x$

We will apply cross multiplication

$10 =3x
\\
x = \frac{10}{3}$

$x = 3.3$

Thus, the approximate input value is 3.3.

6 0

1 month ago

Read 2 more answers