Final answer:
To find tan theta when cos theta = 1/4, use the Pythagorean identity to find sin theta and then divide sin theta by cos theta to get tan theta, which is (sqrt(15)).
Explanation:
To find tan theta when given that cos theta = 1/4 and knowing that theta is between 0 and 90 degrees, we can use the Pythagorean identity for trigonometric functions, which states that sin^2 theta + cos^2 theta = 1. Since we have cos theta, we can solve for sin theta.
First, square cos theta to get cos^2 theta:
cos^2 theta = (1/4)^2 = 1/16
Now, apply the identity:
sin^2 theta = 1 - cos^2 theta = 1 - 1/16 = 15/16
Take the square root to find sin theta (choosing the positive root since theta is between 0 and 90 degrees):
sin theta = √(15/16) = √15/4
Finally, use the definition of tan, which is sin theta / cos theta:
tan theta = sin theta / cos theta = (√15/4) / (1/4) = √15
It takes 8 minutes for Byron to fill the kiddie pool in the backyard using only a handheld hose. When his younger sister is impatient, Byron also uses the lawn sprinkler to add water to the pool so it is filled more quickly. If the hose and sprinkler are used together, it takes 5 minutes to fill the pool. Which equation can be used to determine r, the rate in parts per minute, at which the lawn sprinkler would fill the pool if used alone?
A. 5/8 + 5r = 8
B. 5/8 + 5r = 1
C. 5(5/8) = r
D. 5/8 = 5r
Answer:
B,5/8+5r=8
Step-by-step explanation:
A statistical study concluded that the average fan at a typical sporting event spends approximately $7.50 on concessions. if only one vendor is licensed to sell at a concert that expects a turnout of 10,000, what is the projected sales total for the vendor? a) $7,500 b) $15,000 c) $75,000 d) $150,000
The projected sales total for the vendor at the concert is calculated by multiplying the average concession spending of $7.50 by the expected 10,000 fans, resulting in $75,000 (option c).
To calculate the projected sales total for the vendor at the concert, we need to multiply the average amount spent by each fan on concessions by the total number of fans expected to attend the event. Given that the average fan spends $7.50 on concessions and that there are 10,000 fans expected, the projected sales total can be found as follows:
Projected Sales Total = Average Spend per Fan x Total Number of Fans
Projected Sales Total = $7.50 x 10,000
Projected Sales Total = $75,000
Therefore, the correct answer is (c) $75,000.
how many times greater is the value of the 2 in 204,936 than the value of the 2 in 124,936
3. The roof of a castle tower is shaped like a cone. The base of the cone is 24 m across and the height is 16 m. The slant height of the roof, which is unknown, is the hypotenuse of the right triangle formed with the radius and the height of the cone. (a) Sketch the roof of the castle tower. Label the known lengths as described AND label the unknown length as x. (b) What is the slant height of the roof? SHOW YOUR WORK!
A class has 25 students - 15 girls and 4 boys. 5 girls and 4 boys are wearing blue. a student is picked at random. what is the probability that the studnet is either a boy or girl who is not wearing blue?
0.8 or 80%.
The question is asking for the probability that a randomly chosen student is either a boy or a girl not wearing blue. There are 25 students in total, with 15 girls and 10 boys. Out of these, 5 girls and 4 boys are wearing blue. Therefore, the number of girls not wearing blue is 15 - 5 = 10 girls. Since all boys are considered in the probability, regardless of what they wear, we have 10 boys. So, we have 10 girls not wearing blue and 10 boys, totalling 20 students that match the criteria out of 25.
The probability can be calculated as follows:
( P(\text{{boy or girl not wearing blue}}) = \frac{{\text{{number of boys and girls not wearing blue}}}}{{\text{{total number of students}}}} = frac{{20}}{{25}} = 0.8 ) or 80%.
Therefore, the probability that a student picked at random is either a boy or a girl who is not wearing blue is 0.8 or 80%.
Please help !!
20 points !!!!
Name the property the equation illusrares 8+3.4=3.4+8
Which functions have real zeros at 1 and 4? Check all that apply.
f(x) = x2 + x + 4
f(x) = x2 – 5x + 4
f(x) = x2 + 3x – 4
f(x) = –2x2 + 10x – 8
f(x) = –4x2 – 16x – 1
Answer:
To find the zeros of a quadratic function, use the quadratic equation, [tex]x=\frac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]. We find that the eqautions with zeros at 1 and 4 are b) x² -5x + 4 and d) -2x² + 10x - 8.
Step-by-step explanation:
a) x² + x + 4 --
[tex]x = \frac{-1 \pm \sqrt{1^2-4*1*4} }{2*1}\\x=\frac{-1 \pm \sqrt{1-16}}{2}[/tex]
Because the discriminant (the value inside the square root) is negative, this equation does not have real zeros, so it is not the answer.
b) x² - 5x + 4 --
[tex]x = \frac{5 \pm \sqrt{(-5)^2-4*1*4}}{2*1} \\x=\frac{5 \pm \sqrt{25-16}}{2} \\x = \frac{5 \pm 3}{2}[/tex]
Now, we calculate the two zeros by adding and subtracting the 3.
[tex]x = \frac{5+3}{2} \\x= \frac{8}{2} = 4\\\\x= \frac{5-3}{2} \\x= \frac{2}{2}=1[/tex]
The zeros of this function are 1 and 4, so it is included in our answer.
c) x² + 3x - 4 --
[tex]x = \frac{-3 \pm \sqrt{3^2-4*1*-4}}{2*1} \\x = \frac{-3 \pm \sqrt{9+16}}{2} \\x= \frac{-3 \pm 5}{2}\\\\x=\frac{-3+5}{2}=1\\x=\frac{-3-5}{2} = -4[/tex]
The zeros of this function are -4 and 1, so it is not the answer.
d) -2x² + 10x - 8 --
[tex]x = \frac{-10 \pm \sqrt{10^2-4*(-2)*(-8)} }{2*(-2)} \\x=\frac{-10 \pm \sqrt{100-64} }{-4} \\x = \frac{-10 \pm 6}{-4} \\\\x=\frac{-10 + 6}{-4} =1\\x = \frac{-10-6}{-4} =4[/tex]
The zeros of this function are 1 and 4, so it is included in our answer.
Graph the function f(x)=−14x−2. Use the line tool and select two points to graph.
The graph of the function (f(x) = -14x - 2) is attached below and the two points from which line passes are (-0.143,0) and (0,-2).
Given :
Equation -- f(x) = -14x - 2
The following steps can be used in order to sketch the graph of the given function:
Step 1 - Write the given function.
f(x) = -14x - 2
Step 2 - Now, evaluate the x-intercept of the above function.
0 = -14x - 2
x = -1/7
Step 3 - Now, determine the y-intercept of the given function.
f(x) = -2
Step 4 - Now, graph the equation of a line that passes through the points (-1/7,0) and (0,-2).
The graph of the function is attached below.
For more information, refer to the link given below:
https://brainly.com/question/14375099
What are the foci of the ellipse given by the equation 100x2 + 64y2 = 6,400?
Quadratic relations and comic sections unit test part 1
11. a. (0, +/- 6)
James pays $120.00 for golf clubs that are on sale fo 20% off at golf pros. At nine iron ,the same clubs cost $8.00'less than they cost at golf pros. They are on sale for 13% off
using a fair coin and a fair six-sided number cube, what is the probability of tossing tails and rolling a multiple of 3?
[tex] |\Omega|=2\cdot6=12\\
|A|=1\cdot2=2\\\\
P(A)=\dfrac{2}{12}=\dfrac{1}{6}\approx17% [/tex]
A clown is juggling at a circus. The path of the ball is given by the parametric equations x=2cos t+2 and y=3sin t+3. In what direction is the ball moving?
-up and to the right
-counterclockwise
-down and to the right
-clockwise
1. B. Counterclockwise
2. C. (30,401)
3. A. t=2(x-3)
4. C. She should have taken both the positive and negative square root
5. C. y=x^2+8x-25/8
6. D. Hyperbola
7. A. Graph A
How is the graph of y=7x^2+4 different from the graph of y=7x^2
1. Is it shifted 4 units up
2. Is it shifted 4 units down
3. Is it shifted 4 units to the left
4. Is it shifted 4 units to the right
A spherical fish bowl is half-filled with water. The center of the bowl is C, and the length of segment AB is 24 inches, as shown below. Use Twenty two over seven for pi.
A sphere with diameter 24 inches is drawn.
Which of the following can be used to calculate the volume of water inside the fish bowl?
1 over 24 over 322 over 7(12 3)
1 over 24 over 322 over 7(12 2) (24)
1 over 24 over 322 over 7(24 3)
1 over 24 over 322 over 7(24 2) (12)
Answer:
1 over 2 4 over 3 22 over 7 (12^3)
Step-by-step explanation:
Volume of sphere = (4/3)*pi*radius^3
If the sphere has a diameter of 24 inches, then its radius is 12 inches.
The spherical fish bowl is half-filled; then, the volume of water inside the fish bowl is half of the volume of the bowl, that is,
volume of water = (1/2)*(4/3)*pi*radius^3
Replacing with radius value and the given value for pi, we get:
volume of water = (1/2)*(4/3)*(22/7)*(12^3)
Algebra 2 help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Urgent!!!!!!!!!!!!
Which of the following are solutions to the equation below?
Check all that apply.
3x^2 + 27x + 60 = 0
A. 4
B. –4
C. –5
D. 5
E. –27
Answer:
The solutions are B. -4 and C. -5
Step-by-step explanation:
For a quadratic equation of the form [tex]ax^2+bx+c=0[/tex] the solutions are
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
For [tex]\mathrm{}\quad a=3,\:b=27,\:c=60:\quad x_{1,\:2}=\frac{-27\pm \sqrt{27^2-4\cdot \:3\cdot \:60}}{2\cdot \:3}[/tex]
[tex]x_1=\frac{-27+\sqrt{27^2-4\cdot \:3\cdot \:60}}{2\cdot \:3}\\\\x_1=\frac{-27+\sqrt{9}}{2\cdot \:3}\\\\x_1=\frac{-27+3}{2\cdot \:3}\\\\x_1=\frac{-24}{6} = -4[/tex]
[tex]x_2=\frac{-27-\sqrt{27^2-4\cdot \:3\cdot \:60}}{2\cdot \:3}\\\\x_2=\frac{-27-\sqrt{9}}{2\cdot \:3}\\\\x_2=\frac{-27-3}{2\cdot \:3}\\\\x_2=-\frac{30}{6} = -5[/tex]
When two fair dice are rolled, what is the probability that at least one of the numbers will be even??
On the Venn diagram, which region(s) represent the union of Set A and Set B (A⋃B)?
a. II
b. I and III
c. I, II, and III
d. I, II, III, and IV
Answer:
c. I, II, and III
Step-by-step explanation:
The union of two sets includes all elements from one set and all elements from the second set.
For our sets, this means all elements of set A, which includes region I and region II. It also means all elements of set B, which includes region III.
Thus the answer is regions I, II and III.
Answer:
C
Step-by-step explanation:
Just took the test
The probability that a dessert sold at a certain café contains strawberries is 26%. The probability that a dessert contains both strawberries and whipped topping is 18%. Find the probability that a randomly chosen strawberry dessert contains whipped topping. Round to the nearest tenth of a percent.
The probability that a strawberry dessert contains whipped topping is approximately 69.2%
We are given that the probability a dessert contains strawberries (P(S)) is 26%, or 0.26, and the probability that a dessert contains both strawberries and whipped topping (P(S and W)) is 18%, or 0.18.
To find the probability that a randomly chosen strawberry dessert contains whipped topping (P(W|S)), we use the conditional probability formula:
[tex]P(W|S) = \frac{P(S and W)}{P(S)}[/tex]
Substituting the given values, we get:
[tex]P(W|S) = \frac{0.18}{0.26} \approx 0.6923[/tex]
Rounding to the nearest tenth of a percent we get the probability that a randomly chosen strawberry dessert contains whipped topping to be 69.2%.
A regular heptagon has a perimeter of 560 centimeters. What is the length of the sides of the heptagon? 56 cm
Which equation represents a parabola with a focus at (0,-2) and a directrix of y=6?
│FV│ = │VD│
Being D the directrix. Given that the focus F is on the y-axis and the directrix is parallel to the x-axis, then the vertex V will also be on this axis, so h = 0.
As │FV│ = │VD│, then:
[tex]k = \frac{6-2}{2}[/tex], that is the middle point of the segment FD, so:
V(0,2)
Now │FV│= │p│= │2-(-2)│=4
Given that the vertex and focus are below the directrix, then the parabola open down, therefore: [tex]p\ \textless \ 0[/tex]
Lastly, the equation is:
[tex]x^{2} = -4(4)(y-2) = -16y+32[/tex]
[tex]y = -\frac{ x^{2} }{16} + 2[/tex]
The equation of a parabola with a focus at (0,-2) and a directrix of y=6 is x^2 = -16(y - 2).
To find the equation of a parabola with a focus at (0,-2) and a directrix of y=6, you need to use the standard form of the equation of a parabola that opens upwards or downwards. The general form of this type of parabola is (x - h)^2 = 4p(y - k), where (h,k) is the vertex of the parabola, and p is the distance from the vertex to the focus (if the parabola opens upwards or downward) or to the directrix (if the parabola opens sideway).
Given that the focus is at (0,-2) and the directrix is at y=6, the vertex of the parabola will be located midway between them. The distance between the focus and directrix is 8 units, so the vertex will be 4 units from each, which puts the vertex at (0, 2). Therefore, h=0 and k=2.
Since the focus is below the directrix, our parabola opens downward, and the value of p is negative. The distance p is half the distance between the focus and directrix, so p=-4. Plugging these values into the general form, we get (x - 0)^2 = 4(-4)(y - 2), which simplifies to x^2 = -16(y - 2).
This is the equation that represents the desired parabola.
If a circle has a radius that is 8 cm long, how long is the circle's diameter?
Answer: just add 8 + 8 and you will get 16
solve 3√5c*7√15c^2 please show your work
Find the length of the curve yequalsthree fifths x superscript 5 divided by 3 baseline minus three fourths x superscript 1 divided by 3 baseline plus 8 for 1less than or equalsxless than or equals27.
The exact value of the arc length of the curve is 149.4 units
How to determine the exact arc length of the curve
From the question, we have the following parameters that can be used in our computation:
[tex]y = \dfrac35x^\frac53 - \dfrac34x^\frac13 + 8[/tex]
Also, we have the interval to be
-1 ≤ x ≤ 27
This means that the x valus are
x = -1 to x = 27
The arc length of the curve can be calculated using
[tex]\text{Length} = \int\limits^a_b {\sqrt{1 + ((dy)/(dx))^2}} \, dx[/tex]
Recall that
[tex]y = \dfrac35x^\frac53 - \dfrac34x^\frac13 + 8[/tex]
So, we have
[tex]\dfrac{dy}{dy} = x^\frac{2}{3}-\dfrac{1}{4x^\frac{2}{3}}[/tex]
This means that
[tex]\text{Length} = \int\limits^{27}_{-1} {\sqrt{1 + (x^\frac{2}{3}-\dfrac{1}{4x^\frac{2}{3}})^2}} \, dx[/tex]
Using a graphing tool, we have the integrand to be
[tex]\text{Length} = \dfrac{12x^\frac{5}{3}+15\sqrt[3]{x}}{20}|\limits^{27}_{-1}[/tex]
Expand and evaluate
[tex]\text{Length} = 149.4[/tex]
Hence, the exact arc length of the curve is 149.4 units
*Write An inequality then solve for the width.* The length of a rectangle is 12 more than its width. what values of the width will make the perimeter less than 96 feet? (Will give brainliest to best answer)
PLEASE HELP!! WILL GIVE BRAINLIEST!!!!!!!
A car's radiation fan has five equally spaced blades. In how many different rotations less than 360° can you rotate the fan onto itself?
4
2
3
1
PLEASE PLEASE HELP ME!!!
The scatter plot shows the number of football and baseball cards collected by a sample of third grade children. A coordinate plane titled Number of Football and Baseball Cards Collected with x and y axis ranging from 0 to 100 in increments of 10. The y axis is titled Baseball cards and the x axis is titled Football cards. The coordinate plane contains 11 points. Begin ordered pair 10 comma 60 end ordered pair labeled F. Begin ordered pair 10 comma 90 end ordered pair labeled A. Begin ordered pair 20 comma 40 end ordered pair labeled K. Begin ordered pair 30 comma 40 end ordered pair labeled E. Begin ordered pair 30 comma 60 end ordered pair labeled J. Begin ordered pair 40 comma 40 end ordered pair labeled D. Begin ordered pair 50 comma 40 end ordered pair labeled C. Begin ordered pair 60 comma 20 end ordered pair labeled H. Begin ordered pair 70 comma 20 end ordered pair labeled I. Begin ordered pair 80 comma 20 end ordered pair labeled G. Begin ordered pair 80 comma 50 end ordered pair labeled B. Which children collected more football than baseball cards? Dan, Simian, Jason, Peter Monique, Jordan, Peter, Dan, Simian, Jason Ruso, Ryan, Monique, Jordan, Peter Dan, Simian, Ken, Jimmy, Jason Name Label Dan A Peter B Ruso C Dyna D Jimmy E Simian F Jordan G Ryan H Monique I Jason J Ken K
The children who collected more football than baseball cards are:
Ruso, Ryan , Monique , Jordan , Peter.
Step-by-step explanation:We are given a set of values as:
( Football cards,Baseball cards) Letter Name
(10,60) F Simian
(10,90) A Dan
(20,40) K Ken
(30,40) E Jimmy
(30,60) J Jason
(40,40) D Dyna
(50,40) C Ruso
(60,20) H Ryan
(70,20) I Monique
(80,20) G Jordan
(80,50) B Peter
Hence, children who collected more football then baseball cards are the one whose first value of the ordered pair is more than the other.
Hence, They are:
(50,40) C Ruso
(60,20) H Ryan
(70,20) I Monique
(80,20) G Jordan
(80,50) B Peter.
what does x2 + 11x + 24 look like on a graph
A supporting goods store sells 2 fishing reels and 5 fishing rods for $243. Later, they still 8 fishing reels and 6 fishing rods for $538. Find the price of each item.