What is the value of z?
61°
310
to
25°
Lo
O
zº
N

Answer:

43.5F

Step-by-step explanation:

All you need to do is subtract 15.70 from 59.20

(a) The times at which the blood pressure is 100 mmHg are t = 0 and t = 1/70.

b) The time at which the blood pressure is 120 mmHg is t = 1/140.

c)The times at which the blood pressure is between 100 and 105 mmHg are t = arcsin(1/4)/70π and t = 1 - arcsin(1/4)/70π

(a) To determine the times at which the blood pressure is 100 mmHg in the interval [0, 1], we need to find the values of t that satisfy the equation P(t) = 100:
100 = 20 sin(70πt) + 100
0 = 20 sin(70πt)
sin(70πt) = 0
70πt = nπ, where n is an integer
t = n/70
In the interval [0, 1], the possible values of n are 0 and 1. Therefore, the times at which the blood pressure is 100 mmHg are t = 0 and t = 1/70.

(b) To determine the times at which the blood pressure is 120 mmHg in the interval [0, 1], we need to find the values of t that satisfy the equation P(t) = 120:
120 = 20 sin(70πt) + 100
20 = 20 sin(70πt)
sin(70πt) = 1
70πt = (2n+1)π/2, where n is an integer
t = (2n+1)/140
In the interval [0, 1], the possible value of n is 0. Therefore, the time at which the blood pressure is 120 mmHg is t = 1/140.

(c) To determine the times at which the blood pressure is between 100 and 105 mmHg in the interval [0, 1], we need to find the values of t that satisfy the inequality 100 < P(t) < 105:
100 < 20 sin(70πt) + 100 < 105
0 < 20 sin(70πt) < 5
0 < sin(70πt) < 1/4
Since sin(70πt) is positive and less than 1/4 in the interval [0, 1], we need to find the values of t that satisfy the equation sin(70πt) = 1/4:
sin(70πt) = 1/4
70πt = arcsin(1/4)
t = arcsin(1/4)/70π
The times at which the blood pressure is between 100 and 105 mmHg are t = arcsin(1/4)/70π and t = 1 - arcsin(1/4)/70π.

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Answer:

done by a calculator =w=

Answer:

100 ft high

Step-by-step explanation:

you multiply

Distance from the top of the pole to the end of the shadow is 20.62 ft.

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

Height of pole = 20ft

Length of the shadow = 5ft

Let distance from the top of the pole to the end of the shadow be x

then by Pythagoras theorem

Hypotenuse² = Base² + Perpendicular²

x² = 5² + 20²

x² = 25 + 400

x = √425

x = 20.62 ft

Hence, 20.62 feet is distance from the top of the pole to the end of shadow.

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Answer:

ok, the y intercept is 0.9

Step-by-step explanation:

what are the dropdowns

60%

Hi there !

5 ........... 100%

3 .................x%

x = 3×100/5

= 300/5

= 60%

Good luck !

The lower bound of the 95% confidence interval is given as follows:

7.981 mm.

The level of confidence of the statement is of 95%.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 100 - 1 = 99 df, is t = 1.9842.

The parameters for this problem are given as follows:

\(\overline{x} = 8.1, s = 0.6, n = 100\)

Hence the lower bound of the interval is given as follows:

8.1 - 1.9842 x 0.6/10 = 7.981 mm.

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Answer: line of reflection: x = 1/2 (look at the image for the explanation)

Step-by-step explanation:

Answer:

Her door should be 3cm on scale

The actual dimension of the kitchen table is

\(Length = 1.6m\)

\(Width = 1m\)

Step-by-step explanation:

Given

\(Scale= 1 : 40\)

\(Kitchen\ Dimension= 6m\ by\ 2m\)

\(Door\ Width = 1.2m\)

Solving (a): The width of the door on the scale

Represent the scale width with x

So, we have:

\(1 : 40\)

and

\(x : 1.2\)

Equate both ratios

\(1 : 40 = x : 1.2\)

Represent as fraction

\(\frac{1}{40} = \frac{x}{1.2}\)

Solve for x

\(x = \frac{1.2}{40}\)

\(x = 0.03m\)

\(x = 3cm\)

Hence, her door should be 3cm on scale

Solving (b): Actual Dimension of the kitchen table

To solve this, we simply multiply the scale dimensions by 40

\(Length = 4cm * 40\)

\(Length = 160cm\)

\(Length = 1.6m\)

\(Width = 2.5cm * 40\)

\(Width = 100cm\)

\(Width = 1m\)

Hence:

The actual dimension is

\(Length = 1.6m\)

\(Width = 1m\)

Step-by-step explanation:

Maximum area enclosed will be a square enclosure

  since the river is one side , the other three sides of the square will be

       1440 / 3 = 480 ft long

Square with sides 480 ft

area =480 x 480 = 230 400 ft^2

We are given the angles 50, 40, and 90. To determine if these angles form a triangle we need to add them all together and if the answer is 180, then they do form a triangle:

Therefore, these angles form a triangle. This triangle is not unique since all the triangles with these angles form a set of similar triangles.

Answer:

2.5 feet

Step-by-step explanation:

Answer:

2.5 feet

Step-by-step explanation:

\( \frac{30}{12} = 2.5\)

The function is decreasing exponentially at a rate of 85% every hour.

f(t) = 8000 \((0.15)^{24t}\)

Here, 0.15 is the change the factor and since 0.15 is less than 1. Therefore , the it represents negative rate of change in the quantity that is decreasing.

Now, put t = 1/24 days

f(t) = 8000 \((0.15)^{24 * 1/24}\)

    = 8000 (0.15)

    = 1200

Now, put t = 2/24 days

f(t) = 8000 \((0.15)^{2 * 2/24\\}\)

     = 8000 \((0.15)^{2}\)  

     = 180

So, change in 1 hour = 1200 - 180

                                   = 1020

Rate of change of decrease = 1020 x 100 / 1200

                                                = 85%

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Answer:

the one you have selected is correct

Step-by-step explanation:

just remember when a number has absolute value bars around them it basically just makes it positive.

(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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The largest interval I over which the solution is defined is (-∞, ∞).               I = (-∞, ∞)

To solve the given initial-value problem, we can use the method of separation of variables as follows:
1. Separate the variables by moving all terms with y to the left side of the equation and all terms with x to the right side:
y/y' = ex/x
2. Integrate both sides of the equation with respect to their respective variables:
∫y/y' dy = ∫ex/x d
ln(y) = ex + C
3. Solve for y:
y = e^(ex + C)
4. Use the initial condition y(1) = 9 to find the value of C:
9 = e^(e + C)
C = ln(9) - e
5. Substitute the value of C back into the equation for y:
y = e^(ex + ln(9) - e)
6. Simplify the equation:
y = 9e^(ex - e)
7. The largest interval I over which the solution is defined is (-∞, ∞), since there are no restrictions on the values of x or y therefore, the solution to the initial-value problem is y(x) = 9e^(ex - e) and the largest interval I over which the solution is defined is (-∞, ∞).

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Answer:

The mistake is that you are supposed to do the 15 - 4 first, getting 11, then applying the distributive property and multiplying 11 by 1x and 3.

Hope this helped! Have a nice day, and plz mark as brainliest if correct!!!

-Lil G

Given the initial number 814,593, notice that it is equivalent to

Therefore, the number 4 is in the one thousands place.

The value x in the secant line using the Intersecting btheorem is 19.

Intersecting secants theorem states that " If two secant line segments are drawn to a circle from an exterior point, then the product of the measures of one  of secant line segment and its external secant line segment is the same or equal to the product of the measures of the other secant line segment and its external line secant segment.

From the image;

External line segement of the first secant line = 8

First sectant line segment = ( x + 8 )

External line segement of the second secant line = 9

First sectant line segment = ( 15 + 9 )

Using the Intersecting secants theorem:

8 ×  ( x + 8 ) = 9 × ( 15 + 9 )

Solve for x:

8x + 64 = 135 + 81

8x + 64 = 216

8x = 216 - 64

8x = 152

x = 152/8

x = 19

Therefore, the value of x is 19.

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The vector spaces that are isomorphic to ℝ^6 are (b) P6, (d) M6,1, and (g) {(x1, x2, x3, 0, x5, x6): xi is a real number}.

The vector spaces that are isomorphic to ℝ^6 are P6, M6,1, and {(x1, x2, x3, 0, x5, x6): xi is a real number}.

In the polynomial space P6, the vectors represent polynomials of degree at most 6. In the matrix space M6,1, the vectors represent 6x1 matrices. In the set {(x1, x2, x3, 0, x5, x6): xi is a real number}, the vectors are in ℝ^6 but have the fourth component fixed at 0.

These vector spaces have the same dimension as ℝ^6 (which is 6) and can be bijectively mapped to each other while preserving vector addition and scalar multiplication operations. Therefore, they are isomorphic to ℝ^6.

The other options, M2,3, C[0, 6], P5, and C′[−3, 3], are not isomorphic to ℝ^6 because they either have different dimensions or represent different types of objects.

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The points on the curve where the tangent is horizontal: (1, 0) & (-1, 0),  and where the tangent is vertical: (0, 1) & (0, -1)

To find the points on the curve x=cos(theta) where the tangent is horizontal or vertical, we need to find the derivative of x with respect to theta.

Taking the derivative of x with respect to theta, we get:

dx/dtheta = -sin(theta)

When the tangent is horizontal, the derivative is equal to zero. So we need to solve the equation -sin(theta) = 0 for theta.

This equation is true when theta = n*pi, where n is an integer. So the points on the curve x=cos(theta) where the tangent is horizontal are:

(1, 0) for n=2k, where k is an integer

(-1, 0) for n=2k+1, where k is an integer

When the tangent is vertical, the derivative is undefined. This happens when cos(theta) = 0, which is true when theta = (2k+1)*pi/2, where k is an integer.

So the points on the curve x=cos(theta) where the tangent is vertical are:

(0, 1) for n=2k+1, where k is an integer

(0, -1) for n=2k, where k is an integer

Therefore, the points on the curve where the tangent is horizontal are (1, 0) and (-1, 0), and the points on the curve where the tangent is vertical are (0, 1) and (0, -1).

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Answer:

9 cups of milk is used

Step-by-step explanation:

1/2 + 1/2 + 1/2 = 1 1/2

3×3 = 9

Answer:

Now, check another value for the variable.

When w = 2, the first expression is  

✔ 11

.

When w = 2, the second expression is  

✔ 11

.

Therefore, the expressions are  

✔ equivalent

.

Step-by-step explanation:

Answer:

1. 11

2. 11

3. Equivalent

Step-by-step explanation:

There are 4,608 different ways that the class can elect a president, vice president, and secretary.

To find the number of different ways that a class of 18 students can elect a president, vice president, and secretary, we will use the formula for permutations, which is given by -

nPk = n! / (n - k)!

where n is the total number of items and k is the number of items to be selected in a specific order.

In this case, we are given n = 18 students and k = 3 positions.

Thus, the number of different ways to elect a president, vice president, and secretary will be -

18P3 = 18! / (18 - 3)! = 18! / 15! = 18 x 17 x 16 = 4,608

Therefore, there are 4,608 different ways that the class can elect a president, vice president, and secretary.

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For a small h, the formula f(x + h) - f(x - h)/2h should give a reasonable approximation of f'(x).

slope of the secant line that goes from x - h to x + h. Its limit as h goes to 0 is the average rate of change of f(x) over the interval [x - h, x + h]. If f(x) is continuous and differentiable, then the average rate of change over a small interval should be close to the instantaneous rate of change at x, which is f'(x). Therefore, for a small h, the formula f(x + h) - f(x - h)/2h should give a reasonable approximation of f'(x).

So the correct answer is: C. The formula f(x + h) - f(x)/h gives the slope of the tangent line that goes from x to x + h. Its limit as h goes to 0 is f'(x). The formula f(x + h) - f(x - h)/2h gives the slope of the secant line that goes from x - h to x + h. Its limit as h goes to 0 is the average rate of change of f(x) over the interval [x - h, x + h]. If f(x) is continuous and differentiable, then the average rate of change over a small interval should be close to the instantaneous rate of change at x, which is f'(x).

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In this problem, we need to find the equation and the graph of a parabola given the focus and the directrix.

Sometimes it's best to start with graphing the given information to determine if the graph is a horizontal or vertical parabola. So, we'll have:

Since the focus is always inside the parabola and the directrix is outside the parabola, we know this will be a vertical parabola. Depending on the text, this standard formula may look different. For our purposes, the standard form of a vertical parabola is:

Where (h,k) is the vertex.

The vertex is typically the same distance from both the focus and the directrix, so we can find the distance between them and divide by 2.

The vertex will be at (-2,3):

Now we can substitute the vertex into our standard form knowing (h,k) = (-2, 3):

Next, we need to find the value of p for our equation.

P is the distance from the vertex to the focus. Since our vertex is at (-2,3) and our focus is at (-2,4), the difference between the y-values shows a distance of 1.

Since p=1,

Our final graph is:

The contribution margin ratio for The Halpert Group is approximately 0.63. Therefore, option B. is correct.

To find the contribution margin ratio for The Halpert Group, we'll use the formula:

Contribution Margin Ratio = (Selling Price - Variable Cost) / Selling Price.

Identify the selling price and variable cost per unit.
Selling Price = $20
Variable Cost = $7

Calculate the contribution margin per unit.
Contribution Margin = Selling Price - Variable Cost

Contribution Margin = $20 - $7

Contribution Margin = $13

Calculate the contribution margin ratio.
Contribution Margin Ratio = Contribution Margin / Selling Price

Contribution Margin Ratio = $13 / $20

Contribution Margin Ratio = 0.65

The closest answer to 0.65 is option B. 0.63. Therefore, the contribution margin ratio for The Halpert Group is approximately 0.63.

So, option B. is correct.

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