The correct answer is tan Theta = 12/5.
The task is to find the value of tan Theta given that in a position where its terminal side lies in Quadrant 3 and sine is -12/13. In the third quadrant, both sine and tangent are negative, so we expect a negative ratio for tan Theta. Since sine equals opposite over hypotenuse, we have:
sin Theta = opposite/hypotenuse = -12/13
The negative sign indicates that the opposite side is in the negative direction (downward in this case).
To find tan Theta, we'll use the Pythagorean theorem to find the length of the adjacent side:
opposite^2 + adjacent^2 = hypotenuse^2
(-12)^2 + adjacent^2 = 13^2
144 + adjacent^2 = 169
adjacent^2 = 169 - 144
adjacent^2 = 25
adjacent = [tex]\sqrt{5}[/tex]
Because we're in the third quadrant, where the x-coordinate (adjacent side in the context of the unit circle) is negative, adjacent = -5.
Now, tan Theta = opposite/adjacent = -12/-5 = 12/5.
Therefore, the correct answer is D. 12/5.
Evelyn is working two summer jobs, making $18 per hour lifeguarding and making $11 per hour tutoring. In a given week, she can work a maximum of 15 total hours and must earn no less than $200. If Evelyn worked 8 hours lifeguarding, determine the maximum number of whole hours tutoring that she can work and still meet her requirements.
Given Evelyn's hourly rates for both of her jobs and the total number of working hours she has, Evelyn can work a maximum of 7 hours tutoring if she has already spent 8 hours lifeguarding.
Explanation:To solve this problem, we first calculate the total earning from lifeguarding by multiplying the hourly rate by the number of hours she worked, which results in $18 * 8 = $144. The minimum total earning she must make is $200, so she still needs to earn $200 - $144 = $56. Since she is making $11 per tutoring hour, she will need to work a minimum of $56 / 11 which is approximately 5 hours. However, these are still part of the total of 15 hours maximum she can work, and she has already worked 8 hours lifeguarding, meaning she can work at most 15 - 8 = 7 hours tutoring in the remaining time.
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The maximum number of whole hours tutoring that Evelyn can work while still meeting her requirements is 5 hours.
To solve this problem, we can use a combination of inequalities to represent the given constraints.
We need to solve these inequalities simultaneously to find the maximum number of whole hours Evelyn can work as a tutor.
1. The first inequality:
[tex]\[ x + 8 \leq 15 \][/tex]
[tex]\[ x \leq 15 - 8 \][/tex]
[tex]\[ x \leq 7 \][/tex]
2. The second inequality:
[tex]\[ 18(8) + 11x \geq 200 \][/tex]
[tex]\[ x \geq \frac{56}{11} \][/tex]
[tex]\[ x \geq 5.09 \][/tex]
Since the number of tutoring hours must be a whole number, Evelyn can work a maximum of 5 whole hours tutoring and still meet her requirements.
Therefore, the maximum number of whole hours tutoring that Evelyn can work while still meeting her requirements is 5 hours.
what is the intercept??
Answer:
For the first part the intercept is -1 and the second part the anwser is -5
Step-by-step explanation:
This is becuase when dealing with slopes and the slope intercept form (y=mx+b) whatever is B in the said equation your are dealing with is the y intercept
When a group of people were tested for a rare disease, 99.6 percent of them
were found not to have the disease If the 10 people did have the disease, how
many people were tested? *
Answer:
2600 were tested
99.6% of 2590 = - 10 + 10 = 2600 people.
99.6% of 2600 = 2589.6
Step-by-step explanation:
10 = positive = inverse of 99.6 = 0.4
0.4 x 1000 = 400
So we need an odd number ie) 3,000 minus 400 to make 10 extra when inverse is missing. = 3000 - 400 = 2600
99.6% of 2600 = 2589.6
Is the lowest number.
the lateral area of a cone is 558pi cm^2 the radius is 31 cm. find the slant height to the nearest tenth
The slant height of the cone is 39.7 cm
Explanation:
Given:
Lateral surface area of a cone = 558π cm²
Radius, r = 31 cm
Slant height, l = ?
We know:
[tex]A = \pi r\sqrt{h^2+r^2}[/tex]
Where,
h is the height of the cone
r is the radius
Solving the equation further:
[tex]558\pi = \pi r\sqrt{h^2+r^2} \\\\558 = 31\sqrt{h^2+(31)^2} \\\\(18)^2 = h^2 + 961\\\\324 = h^2+ 961\\\\h = 25.23[/tex]
Lateral height, H = ?
Applying pythagoras theorm,
(H)² = (h)² + (r)²
(H)² = (25.23)² + (31)²
(H)² = 636.55 + 961
(H)² = 1597.55
H = 39.7 cm
Therefore, the slant height of the cone is 39.7 cm
−4 = 2t − 2 what does t equal
Answer:
t = -1
Step-by-step explanation:
-4 = 2t - 2
2t = -2
t = -1
Can I get brainliest
Answer:
t = -1
Step-by-step explanation:
-4 = 2t - 2
Add 2 on both sides.
-4 + 2 = 2t - 2 + 2
-2 = 2t
Divide both sides by 2.
-2/2 = (2t)/2
-1 = t
if you can solve this ill give you the brainliest.
Answer:
1
Step-by-step explanation:
Use PEMDAS
(Solve division first)
9 - 9 + 1 =
(Solve from left to right)
1
What is the sum of the measures of the exterior angles of this triangle?
A triangle has angles A, C, 51 degrees. Angle A has exterior angle B and angle C has an exterior angle with measure of 112 degrees.
The measure of ∠B is 119°.
What is the exterior angle?An exterior angle is a measure of rotation between one extended side(we extend it virtually) of the polygon with its adjacent side which is not extended.
All the exterior angles are of the same measure, and therefore, their measure is (360/n)°.
The angle adjacent to 112° will form a straight angle along with 112° adding to 180° which makes ∠C=68°
Then;
a+c+51°= 180°
a+68°+51° = 180°
a+119° = 180°
a = 180° - 119°
a = 61°
Now,
a+b = 180°
61+b = 180
b = 180-61
b = 119°
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Answer:
119
Step-by-step explanation:
100 on edge
identify the arc length of TV in terms of pie with radius of 5
Explain how to write an equivalent expression using the
distributive property.
2(11 + y)
Answer:
I believe this is the answer your looking for? 22 + 2y
Step-by-step explanation:
Answer:
To use the distributive property, distribute multiplication by 2 to both terms inside the parentheses.
The products are 2(11) and 2(y).
The equivalent expression is 22 + 2y.
Step-by-step explanation:
hope this helps!
Find the Area of the figure below, composed of a rectangle and two semicircles.
Round to the nearest tenths place.
13
Answer:
154.29
Step-by-step explanation:
The area of rectangle is given by
Ar=lw
Area of semi circle is given by
[tex]A_c=0.5\pi r^{2}[/tex]
Since there are two semi-circles then the area will be
[tex]A_c=2*0.5\pi r^{2}=\pi r^{2}[/tex]
The diameter is given as 8 units hence the radius is half the diameter, 4 units
Length is given as 13 units and width is diameter which is equal to 8 units
Area of rectangle will be 13*8=104 square units
Area of the two semi-circles will be
[tex]A==\pi 4^{2}=50.285714285713[/tex]
Total area wi be 104+50.285714285713=154.285714285713 square units
Rounded off as 154.29 square units
Answer:
The answer is 154.3
The probability distribution below is
A bar graph has X on the x-axis, from 1 to 6, and P x (x) on the y-axis, from 0 to 0.4 in increments of 0.05. The probability of 1 through 6 is: 0.02, 0.04, 0.15, 0.18, 0.25, 0.36.
Answer: Negatively Skewed
first option
Step-by-step explanation:
just did it on edge
Answer:
A
Step-by-step explanation:
bob needs to be at school by 7:00 it takes him 1 hour and 21 minutes to get there. his morning routine takes 30 minutes. what time should bob leave the house
Answer:
5:00
Step-by-step explanation:
1 hour 21 minutes = 1,35 hours
30 minutes = 0,5 hours
1,35-0,5=0,85 hours he needs to get to school
7-0,85=6,15
6,15 = 6 hours 9 minutes
In 6 hours 9 minutes he needs to leave the house
find the length of bc
give your answer to 3 signifcant figures
Using the cosine ratio, side BC in the right-angled triangle is approximately 19.4 cm when rounded to three significant figures.
In the right-angled triangle ABC, where angle A is 90 degrees, side AB is the base, side AC is the perpendicular, and side BC is the hypotenuse, we can use trigonometry to find the length of BC.
The cosine ratio (cos) relates the adjacent side to the hypotenuse in a right-angled triangle. In this case, cos(B) = AB/BC. To find BC, rearrange the formula to BC = AB/cos(B).
Given AB = 6.3 cm and angle B = 71 degrees, substitute these values into the formula:
[tex]\[ BC = \frac{6.3 \, \text{cm}}{\cos(71^\circ)} \][/tex]
Using a calculator, find that cos(71 degrees) is approximately 0.325. Now, divide 6.3 cm by this value:
[tex]\[ BC \approx \frac{6.3 \, \text{cm}}{0.325} \approx 19.385 \, \text{cm} \][/tex]
Rounded to three significant figures, the length of side BC is approximately 19.4 cm.
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A sphere has a volume of 4500pi cubic feet what is the radius of the sphere
Given a volume of 4500π cubic feet, the radius is found to be approximately 15 feet after solving the equation.
To find the radius of a sphere given its volume, we use the formula for the volume of a sphere: V = (4/3)πr³. In this case, the given volume is 4500π cubic feet. To solve for the radius, we can set up the equation as follows:
V = (4/3)πr³
4500π = (4/3)πr³
To isolate r³, we divide both sides by π and then multiply by 3/4:
4500 = (4/3)r³
(3/4) * 4500 = r³
3375 = r³
Now, we take the cube root of both sides to find the radius:
r = ³√3375
r ≈ 15 feet
Therefore, the radius of the sphere is approximately 15 feet.
the radius of the sphere is 15 feet.
The formula for the volume [tex](\( V \))[/tex] of a sphere in terms of its radius [tex](\( r \))[/tex] is:
[tex]\[ V = \frac{4}{3}\pi r^3 \][/tex]
Given that the volume of the sphere is [tex]\( 4500\pi \)[/tex] cubic feet, we can set up the equation:
[tex]\[ 4500\pi = \frac{4}{3}\pi r^3 \][/tex]
To find the radius [tex]\( r \)[/tex], we need to isolate it in the equation. First, let's cancel out [tex]\( \pi \):[/tex]
[tex]\[ \frac{4500\pi}{\pi} = \frac{4}{3} r^3 \][/tex]
[tex]\[ 4500 = \frac{4}{3} r^3 \][/tex]
Now, to solve for [tex]\( r \)[/tex], we'll multiply both sides by [tex]\( \frac{3}{4} \)[/tex] to isolate [tex]\( r^3 \):[/tex]
[tex]\[ r^3 = \frac{4500 \times 3}{4} \][/tex]
[tex]\[ r^3 = \frac{13500}{4} \][/tex]
[tex]\[ r^3 = 3375 \][/tex]
Now, to find ( r ), we'll take the cube root of both sides:
[tex]\[ r = \sqrt[3]{3375} \][/tex]
[tex]\[ r = 15 \][/tex]
So, the radius of the sphere is 15 feet.
giving 35 points if your wrong your getting reported !
Answer:
The answer is 1680m3
Step-by-step explanation:
h×b×1/2×w
What is the independent variable?
Answer:
Step-by-step explanation:
Well, I'm not sure if I'm correct, but from what I've learned, and independent variable is first which could be the temperature.
help plzz i'll give you 12 points to answer this.
Answer:
it is answer 3
Step-by-step explanation:
Answer:
The answer is c
Step-by-step explanation:
Tyler's grocery receipt shows a charge of $0.25 for every apple he purchased.
Let g represent the amount on the grocery receipt.
Let a represent the number of apples purchased
Which is the independent variable?
the amount of the grocery bill
the cost of an apple
the weight of the apples
the number of apples purchased
The number of apples Tyler purchased is the dependent variable.
What is a variable?The alphabetic character that expresses a numerical value or a number is known as a variable in mathematics.
A representation of an unknown numerical value in an equation or algebraic statement by a symbol, typically a letter. A variable can be defined as a quantity that is changeable and not fixed.
Given:
Tyler’s grocery receipt shows a charge of $0.25 for every apple he purchased.
'g' represent the amount on the grocery receipt.
'a' represent the number of apples purchased.
Therefore, 'a' is the variable here.
So, the amount of apple is independent variable but the purchased values if dependent variable.
Thus, the number of apple Tyler purchased is the dependent variable.
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Final answer:
The independent variable is the number of apples purchased, as it determines the dependent variable, which is the total amount spent on apples in the grocery bill.
Explanation:
The independent variable in this scenario is the number of apples purchased (represented by a). This is because the independent variable is the one that is changed or controlled in a scientific experiment to test the effects on the dependent variable. In this case, Tyler decides how many apples to buy, and that decision directly affects the total cost, which is the dependent variable (g). The price of an apple, the weight of the apples, and the amount on the grocery bill are all dependent on the number of apples Tyler chooses to purchase. To find the total amount spent on apples, one would multiply the number of apples purchased by the cost per apple.
what rule matches the function represented by the table?
Let's try a line
y = mx + b
From (0,4):
4 = 0x + b
b = 4
So far we have
y = mx + 4
From (1,1)
1 = m(1) + 4
-3 = m
Our rule is y = -3 x + 4
Let's check the other points:
-3(-4)+4 = 12+4 = 16 good
-3(4)+4 = -12+4 = -8 good
-3(9) + 4 = -23 good
Answer: y = -3 x + 4
The rule matching a function as shown by a table can be determined by analyzing the difference and relationship between x-values and y-values. This might represent a linear, exponential, or quadratic relationship, which can be described by a range of mathematical equations.
Explanation:Unfortunately, without having the actual table and data, it is hard to give an accurate rule for the function. However, generally, in order to define a rule that matches a function represented by a table, you would need to discern a pattern between the inputs (often represented by the x-values) and the outputs (represented by the y-values).
In some cases, this might be a simple linear rule where each step in the x-values increases or decreases the y-values by a consistent rate; this would represent a formula of the format y = mx + b, where m is the change in y over the change in x, and b is the y-value when x = 0. Alternately, more complex relationships (such as exponential or quadratic rules) might be represented and would need different formulas to be described properly.
Determining the rule can often involve finding the rate of change between pairs of data points and discerning what kind of relationship this reveals. The explanation and answer would then match this established pattern.
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Can someone explain this to me please? It would be so much help : )
Minimum price: Increases.
Maximum price: Remains the same.
Range: Increases.
Mean (Average) price: Cannot be determined.
When the kid's meal is added to the menu, the effect on the statistics of the meal prices can be determined as follows:
Minimum Price: Increases
Adding the kid's meal, which costs $2.35, to the menu will increase the minimum price.
Therefore, the value of the minimum price statistic will increase.
Maximum Price: Increases
Since the maximum price of the kid's meal ($2.35) is lower than the previous maximum price of $12.10, adding the kid's meal to the menu will not change the maximum price.
Therefore, the value of the maximum price statistic remains the same.
Range: Increases
The range is calculated as the difference between the maximum and minimum prices.
As the minimum price increases while the maximum price remains the same, the difference between them (the range) will increase.
Therefore, the value of the range statistic will increase.
Mean (Average) Price: Cannot be determined
To determine the effect on the mean price, we would need information about the number of meal options available and their individual prices. Without this information, we cannot determine whether the mean price will increase, decrease, or remain the same.
Therefore, the value of the mean price statistic cannot be determined.
In summary:
Minimum price: Increases
Maximum price: Remains the same
Range: Increases
Mean (Average) price: Cannot be determined
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The histogram shows how many jogging runs Maria made for each interval of miles. A histogram titled Maria's Monthly Jogging has miles run on the x-axis and number of runs on the y-axis. 1 to 1.99 miles is 2 runs; 2 to 2.99 miles is 5 runs; 3 to 3.99 miles is 5 runs; 4 to 4.99 miles is 3 runs; 5 to 5.99 miles is 4 runs; 6 to 6.99 is 7 runs; 7 to 7.99 miles is 4 runs. Which statement about the histogram is true? The majority of Maria’s runs were short, two-mile runs. More than half Maria’s runs were less than five miles each. The majority of Maria’s runs were between five and six miles. At least 15 of Maria’s runs were more than four miles each.
Answer:at least 15 of maria's runs were more then four miles each
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
Help asappp plzzzzzzzzzz
Answer: The answer is 175
Step-by-step explanation:
Answer:
175
Step-by-step explanation:
On a map with a scale of 1 in. = 30 miles, the distance between Tarreytown and Hillville is 4 1 /2 in. What is the actual distance between the towns to the nearest mile?
Answer: 135 miles
Step-by-step explanation: I am quick mafs
David purchased a $ 155,000 home with a 7/23 balloon mortgage. His initial rate was 3.5%. At the end of the initial rate, I decided to refinance the balloon payment with a 30-year mortgage fixed at 5%. What is his new mortgage payment? A. $ 696.02 B. $ 707.63 C. $ 707.23 D. $ 654.87
Answer:707.63
Step-by-step explanation:
Answer:798.94
Step-by-step explanation:
Which figure represents the image of trapezoid LMNP after a reflection across the x-axis?
A) figure A
B) figure B
C) figure C
D) figure D
Answer:
A
Step-by-step explanation:
Imagine folding the graph in half on the x-axis and tracing the shape on the other side.
Ps. x-axis is horizontal (left-right), y-axis is vertical (up-down)
The figure that represents the image of trapezoid LMNP after a reflection across the x-axis is the figure A
How to determine the figure?From the figure, we can see that the trapezoid LMNP is the second quadrant.
A reflection across the x-axis will place the trazpezoid in the third quadrant
The figure A is in the third quadrant
Hence, the figure that represents the image of trapezoid LMNP after a reflection across the x-axis is the figure A
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Simplify the following expression:
Sq -16+sq-25+5
The simplified form of the expression √(-16) + √(-25) + 5 is 5 + 9i, where i represents the imaginary unit.
Explanation:The student has asked to simplify the expression Sq -16+sq-25+5. This appears to be a typo, and I believe they are referring to square roots. The correct mathematical expression to simplify should be √(-16) + √(-25) + 5. The simplification of the square roots involving negative numbers results in imaginary numbers because the square root of a negative number is not defined in the set of real numbers but rather in complex numbers. For the given expression, complex numbers and imaginary units ('i', wherein i^2 = -1) will be introduced in simplification:
When we add these results with 5, we obtain 5 + 4i + 5i, which simplifies to 5 + 9i.
What is the image of (4,-7) after a reflection over the y-axis?
Answer:
It would be a point which is at (-4,-7).
The image of the point (4,-7) after a reflection over the y-axis is (-4,-7). This happens because the y-axis is the axis of symmetry during a reflection over this axis, changing the x-coordinate's sign while keeping the y-coordinate constant.
Explanation:The image of a point after a reflection over the y-axis results in the x-coordinate of the point changing its sign. Therefore, the image of the point (4,-7) after a reflection in the y-axis would be (-4,-7). In other words, you move the point 4 units to the left across the y-axis while the y-coordinate remains unchanged.
This process is derived from the concept that the y-axis is the axis of symmetry in a reflection over the y-axis. As such, points on one side of the axis are mirrored on the other side, changing only the sign of the x-coordinate and keeping the y-coordinate constant.
A helpful way to visualize this is by drawing a coordinate grid and plotting the point (4,-7). By reflecting this point over the y-axis, you will see it lands at the point (-4,-7).
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What is science as defined in the intergrated science
Answer:
"Integrated science is defined as a cumulative approach of scientific study that synthesizes the per- spectives of the individual disciplines, and integrates them during all phases of the approach to a question or problem, with the results having an influence on policy and management decision".
Step-by-step explanation:
*Hope this helps*
Science is a systematic study of the natural world that relies on evidence and logical testing of ideas, including various disciplines such as physics, chemistry, and biology.
Science is a systematic examination of the natural world's structure and functioning, including its physical and biological attributes. It is a process of gaining knowledge based on evidence and logical testing of ideas. Natural sciences encompass physics, chemistry, biology, geology, and astronomy and use mathematics and logic as part of their methodologies.
Find the area of the rhombus.
Answer:
The answer is 67.5
Step-by-step explanation:
m∠LONm, angle, L, O, N is a straight angle.
m
∠
L
O
M
=
4
x
+
3
0
∘
m∠LOM=4x+30
∘
m, angle, L, O, M, equals, 4, x, plus, 30, degrees
m
∠
M
O
N
=
8
x
+
9
0
∘
m∠MON=8x+90
∘
m, angle, M, O, N, equals, 8, x, plus, 90, degrees
Find
m
∠
M
O
N
m∠MONm, angle, M, O, N:
Given:
It is given that LON is a straight line. The measure of ∠LOM = (4x + 30)° and the measure of ∠MON = (8x + 90)°
We need to determine the value of m∠MON
Value of x:
Since, LON is a straight line and the angles LOM and MON are linear pairs of angles.
Since, linear pair of angles add up to 180°
Thus, we have;
[tex]\angle LOM+\angle MON=180^{\circ}[/tex]
Substituting the values, we get;
[tex]4x+30+8x+90=180[/tex]
[tex]12x+120=180[/tex]
[tex]12x=60[/tex]
[tex]x=5[/tex]
Thus, the value of x is 5.
Value of m∠MON:
The measure of ∠MON can be determined by substituting x = 5 in the expression (8x + 90)°, we have;
[tex]m\angle MON=(8(5)+90)^{\circ}[/tex]
[tex]m\angle MON=(40+90)^{\circ}[/tex]
[tex]m\angle MON=130^{\circ}[/tex]
Thus, the measure of ∠MON is 130°