Students claim is correct. We can convert tan²θ + 1 = sec²θ to (sin²θ + cos²θ) = 1.
What is Trigonometry?Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles.
Here,
tan²θ + 1 = sec²θ
sin²θ/cos²θ + 1 = 1/cos²θ
By taking LCM, we get
(sin²θ + cos²θ)/cos²θ = 1/cos²θ
(sin²θ + cos²θ) = cos²θ/cos²θ
(sin²θ + cos²θ) = 1
Thus, Students claim is correct. We can convert tan²θ + 1 = sec²θ to (sin²θ + cos²θ) = 1.
Learn more about Trigonometry from:
https://brainly.com/question/22698523
#SPJ1
A company provides snack-sized packages of nuts for its office employees.
employees can choose from among five kinds of nuts. which probabilities
correctly complete this probability distribution for 50 packages of nuts, in the
order listed?
nuts
almonds cashews mixed peanuts pecans
12
10
6
14
8
number of
packages
probability
a. probability 0.32 0.24 0.14 0.2 0.1
The probabilities that correctly complete this probability distribution for 50 packages of nuts will be 0.24, 0.2, 0.12, 0.28, and 0.16.
How to calculate the probability?From the information given, we have to find the probability for each fruit. This will be:
Almond = 12/50 = 0.24
Cashew = 10/50 = 0.2
Mixed = 6/50 = 0.12
Peanut = 14/50 = 0.28
Pecan = 8/50 = 0.16
Therefore, the probabilities that correctly complete this probability distribution for 50 packages of nuts will be 0.24, 0.2, 0.12, 0.28, and 0.16.
Learn more about probability on:
brainly.com/question/24756209
#SPJ1
The graph of y=cosx is translated by (30,-1). What is the equation of the translated graph?
The equation on the graph is shown (I really hope this helps)
Equation of the translated graph is;
⇒y = cos(x - 30) - 1
What is equation of translated graph?
Equation of the translated graph is solved as;
g(x) = f(x + k) + C
Where, k and C are points.
Given that;
The equation is;
y = cos x
Since, Graph of function y = cosx is translated by (30, -1).
So, Equation of translated graph will be;
y = cos(x - 30) - 1
Hence, The equation of the translated graph will be;
⇒ y = cos(x - 30) - 1
Learn more about the translated graph visit:
https://brainly.com/question/25717482
#SPJ2
How many units is -14 away from 0
Answer:
14
Step-by-step explanation:
|-14|=14
The function f(t) represents the cost to connect to the Internet at an online gaming store. It is a function of t, the time
in minutes spent on the Internet.
$0
0
f(t) = $5
30 < 1 ≤ 90
$10
> 90
Which statement is true about the Internet connection cost?
It costs $5 per hour to connect to the Internet at the gaming store.
The first half hour is free, and then it costs $5 per minute to connect to the Internet.
It costs $10 for each 90 minutes spent connected to the Internet at the gaming store.
Any amount of time over an hour and a half would cost $10.
The true statement about the Internet connection cost is D. Any amount of time over an hour and a half would cost $10.
How to explain the cost?In this situation, the function is f (t), when t is a value between 0 and 30. The cost is $0 for the first 30 minutes
When t is a value between 30 and 90, the cost is US$ 5 if the connection takes between 30 and 90 minutes.
Here, the true statement about the Internet connection cost is D. Any amount of time over an hour and a half would cost $10.
Learn more about cost on:
https://brainly.com/question/13862342
#SPJ1
5 less than a number b is 16
[tex] \begin{gathered}\\ \large\dashrightarrow\mathsf { \: \: 5 < b = 6 \: \: \: or \: \: \: b - 5 = 6 } \\ \end{gathered}[/tex]
Solution :-[tex] \begin{gathered}\\ \large\dashrightarrow\mathsf { \: \: b - 5 = 6 } \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \large\dashrightarrow\mathsf { \: \: b = 6 + 5 } \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \large\dashrightarrow \: \: \underline{ \boxed{\mathbf \red{ \: \: b = 11 \: \: }}} \\ \end{gathered}[/tex]
Hence,b is equal to 11 .▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
Additional information[tex]\begin{gathered}\begin{gathered}\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \small \color{blue}{ \underline{\boxed{ \begin{array}{cc} \small \underline{\underline{\bf{ \color{red}{{ \orange \bigstar \: MᴏʀE \: IᴅᴇɴᴛɪᴛɪᴇS \: \orange \bigstar}}}}} \\ \\ \: \frak{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \: \frak{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \: \frak{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \: \frak{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \: \frak{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \: \frak{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \: \frak{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \: \frak{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \\ \: \end{array} }}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered} \: \: [/tex]
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
^०^
Two airplanes leave Chicago at the same time and fly in opposite directions. If one travels at 450 miles per hour and the other at 550 miles per hour, how long will it take for them to be 4000 miles apart
450t+550t=4,000
1000t=4000
t=4000/1000
t=4 hours they will be 4,000 apart.
------------------------------------------
20t+12(4.5-t)=70
20t+54-12t=70
8t=70-54
8t=16
t=16/8
t=2 hours at 20 mph.
proof
20*2+12(4.5-2)=70
40+12(2.5)=70
40+30=70
70=70
In the statement 10 +(-10) =0, how would you describe the -10?
Answer:
-10 is the opposite of 10
Step-by-step explanation:
-10 is the opposite of 10 ,because The sum of a number and its opposite equals to zero.
Mike is adding 145 and 237. his work is shown. how can mike find the sum?
Answer:the answer is 352
Step-by-step explanation: mike can find the sum by adding the two numbers 145+237=352 to make it simpler you can start by adding the hundreds then the tens and then the ones.
please help with geometry!!!! ‼️‼️‼️‼️ i will mark brainliest
Answer:
P = 156 units
Step-by-step explanation:
the perimeter (P) is the sum of the 3 sides of the triangle.
tangents from an external point to the circle are congruent , that is
HK = HJ ( substitute values )
13x - 8 = 7x + 4 ( subtract 7x from both sides )
6x - 8 = 4 ( add 8 to both sides )
6x = 12 ( divide both sides by 2 )
x = 2
Then
HK = HJ = 7x + 4 = 7(2) + 4 = 14 + 4 = 18
and
KI = IL = 21
then
GL = GJ = 60 - 21 = 39
Thus
P = HK + KI + IG + GJ + JH = 18 + 21 + 60 + 39 + 18 = 156 units
a) Work out the size of angle x. b) Give reasons for your answer. + A E C xº B F 105° G D H
Check the picture below.
In 2003 Exxon Mobil received a contract from the government worth $756,733 while Aerospace received a contract from the government worth $539,517. What was the combined total of their contracts?
The combined total of their contracts is $1,296,250
How to determine the combined total?The values of the contracts are given as:
Exxon Mobil= $756,733Aerospace = $539,517The combined total is represented as:
Total = Exxon Mobil + Aerospace
Substitute known values
Total = $756,733 + $539,517
Evaluate the sum
Total = $1,296,250
Hence, the combined total of their contracts is $1,296,250
Read more about sum and total at:
https://brainly.com/question/4916384
#SPJ1
The band is raising money for their spring trip. they need to raise at
least $1500. earlier in the year, they made $575 on their annual fruit sale.
now they are selling donuts, where they will earn $5 profit for each box
of donuts they sell. which inequality could be used in order to
determine the number of boxes of donuts, d, they must sell in order to
meet their goal?
The inequality that can be used to determine the number of boxes of donuts, d, they must sell in order to meet their goal is $1500 ≥ $575 + $5d.
What is the inequality?Here are inequality signs and what they denote:
> means greater than< means less than≥ means greater than or equal to ≤ less than or equal toTotal amount that needs to be raised ≥ amount made at the fruit sale + (profit per box x number of boxes)
$1500 ≥ $575 + $5d
To learn more about inequality, please check: https://brainly.com/question/5031619
#SPJ1
756 x 300??????? ?????????
Answer:
226,800
Step-by-step explanation:
Calculator
Answer:226,800
Step-by-step explanation:
Needing help with these 2 problems
Answer:
15) 3.2
17) 13.4
Step-by-step explanation:
To find the missing lengths, you need to use the Pythagorean theorem:
a² + b² = c²
In this form, "c" represents the length of the hypotenuse and "a" and "b" represent the lengths of the other two sides.
You are trying to find one of the side lengths (not the hypotenuse) in 15). To find the other length, you can plug the other values into the equation and simplify to find "b".
15) a = 4.1 c = 5.2
a² + b² = c² <----- Pythagreom Theorem
(4.1)² + b² = (5.2)² <----- Plug values in for "a" and "c"
16.81 + b² = 27.04 <----- Raise numbers to the power of 2
b² = 10.23 <----- Subtract 16.81 from both sides
b = 3.2 <----- Take the square root of both sides
You are trying to find the hypotenuse in 17). Since you have been given the lengths of the other sides, you can plug them into the equations and simplify to find "c".
17) a = 4.4 b = 12.7
a² + b² = c² <----- Pythagreom Theorem
(4.4)² + (12.7)² = c² <----- Plug values in for "a" and "b"
19.36 + 161.29 = c² <----- Raise numbers to the power of 2
180.65 = c² <----- Add
13.4 = c <----- Take the square root of both sides
1. What is the difference between the altitude rule and the leg rule?
Answer:
The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original triangle
The Leg Rule (or Leg geometric mean theorem) relates the length of each leg of a right triangle with the segments projected by them on the hypotenuse.
Step-by-step explanation:
The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse. Notice the triangle used with this rule. The leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse.
Part F What is the mean absolute deviation for Doctor A’s data set on glasses? What is the mean absolute deviation for Doctor B’s data set on glasses? Write a sentence comparing the variation of the two data sets using their mean absolute deviations.
Doctor A Doctor B
Corrective Lenses Glasses Contacts Corrective Lenses Glasses Contacts
745 643 102 763 651 112
726 634 92 736 625 111
769 670 99 735 622 113
765 658 107 759 624 135
756 636 120 748 631 117
742 624 118 756 621 135
757 641 116 765 653 112
748 655 93 761 647 114
770 649 121 768 646 122
738 629 109 761 646 115
There is more variability on glasses of doctor B's dataset than the glasses of doctor A's dataset
The doctors' mean absolute deviation on glassesThe dataset of doctor A is given as:
643 634 670 658 636 624 641 655 649 629
The dataset of doctor B is given as:
651 625 622 624 631 621 653 647 646 646
Using a statistical calculator, we have:
Doctor A
Doctor A: Mean Absolute Deviation (MAD) = 11.28Doctor B: Mean Absolute Deviation (MAD) = 12Hence, the mean absolute deviation is 11.28 for Doctor A’s and 12 for Doctor B’s data set on glasses
The variation of the two dataIn a dataset, the larger the mean absolute deviations value, the larger the variation.
By comparison, 12 is greater than 11.28
Hence, there is more variability on glasses of doctor B's dataset than the glasses of doctor A's dataset
Read more about mean absolute deviation at:
brainly.com/question/3250070
#SPJ1
A baseball field is a square with sides of length 90 feet. What is the
shortest distance between first base and third base?
A.90
B.180 squared
C.90
D.16200 squared
Multiply.
(3x+2)(2x−5)
6x^2+4x−3
6x^2−10
6x^2−11x−10
6x^2−13x−3
Answer: Heyaa! ^^
Your Answer when multiplied is.. 6x²−11x−10
Step-by-step explanation:
6x^2−11x−10Expand the polynomial using the FOIL method.- FOIL EXPLANATION -
A handy way to remember how to multiply two binomials.It stands for "First, Outer, Inner, Last"
- It is the sum of: -· multiplying the First terms,
· multiplying the Outer terms,
· multiplying the Inner terms, and
· multiplying the Last terms
Hopefully this helps you! ~
What is the range of function g if g(x) =-2f(x-3)
Answer:
If you entered the function correctly there is not a range
Step-by-step explanation:
Answer: {y|-♾<y<0}
Step-by-step explanation: i’m taking this summer school class
Solve the given inequality and graph the solution on a number line. -X/2 -3/2 = 5/2
No Links:
The spin and dine restaurants ice cream for dessert Chloe actually won a bet and gets to spin two spinners disliked one random flavor of ice cream and one random topping. A, how many different possible combinations can she spin. B what is the probability of spinning Chloe's preference vanilla ice cream with chocolate a rainbow sprinkles,
The probability of spinning vanilla ice cream with chocolate a rainbow sprinkles is 1/12
The missing part of the questionFlavor of ice cream: Vanilla, Strawberry, Chocolate
Topping: Rainbow sprinkles, Caramel sauce, Nuts, Cherries
The number of different combinationsUsing the dataset above, we have:
Ice cream = 3
Topping = 4
The number of different combinations is calculated as:
Combination = ice cream * Topping
Evaluate
Combination = 3 * 4
Combination = 12
Hence, the number of different combinations is 12
The probability of spinning vanilla ice cream with chocolate a rainbow sprinklesThe vanilla ice cream with chocolate a rainbow sprinkles is just one of the 12 combinations.
So, the probability is:
P = 1/12
Hence, the probability of spinning vanilla ice cream with chocolate a rainbow sprinkles is 1/12
Read more about probability at:
https://brainly.com/question/27116549
#SPJ1
Given the right triangle, evaluate: sin 0.
Answer: B. 5/13
This is the same as writing [tex]\frac{5}{13}[/tex]
==========================================================
Reason:
We have two given sides of this right triangle. Use the pythagorean theorem to find the missing side.
a = 5 and b = 12 are the two known legs; c is the unknown hypotenuse
[tex]a^2+b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{5^2+12^2}\\\\c = \sqrt{25+144}\\\\c = \sqrt{169}\\\\c = 13\\\\[/tex]
The hypotenuse is exactly 13 units long. This is a 5-12-13 right triangle.
Now we can compute sine of theta
[tex]\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\theta) = \frac{5}{13}\\\\[/tex]
This points us to choice B as the final answer.
----------------
Extra Info (optional)
5/12 is the value of tan(theta) since it's opposite/adjacent12/5 is the value of cot(theta), the reciprocal of tangent12/13 is the value of cos(theta), because cos = adjacent/hypotenuse1 . A rope was 14.35 inches long. Megean cut the rope into 7 pieces of equal length. What was the length of each piece of rope in inches
2. Scott drank 3.5 bottles of water yesterday . Each bottle contained 1.2 pints of water. what was the number of pints of water Scott drank yesterday
Division is one of the four fundamental arithmetic operations. The number of pints of water Scott drank yesterday is 4.2 pints.
What is Division?Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
A rope was 14.35 inches long. Megean cut the rope into 7 pieces of equal length. Therefore, the length of each piece of rope in inches will be,
Length of piece = 14.35 inches/7 = 2.05 inches
Scott drank 3.5 bottles of water yesterday . Each bottle contained 1.2 pints of water. Therefore, the number of pints of water Scott drank yesterday is,
Number of pints = 3.5 bottles × 1.2 pints = 4.2 pints
Hence, The number of pints of water Scott drank yesterday is 4.2 pints.
Learn more about Division:
https://brainly.com/question/369266
#SPJ1
which graph below shows the solutions for the linear inequality y<1/3x-4
Step-by-step explanation:
the answer is C since y is less than. meaning that the line should be dashed and below the graph.
comment if you have any doubts.
Jane earns an annual salary of £14000 and receives
a pay rise of 1.8%
Lenny earns an annual salary of £11000 and
receives a pay rise of 1.7%
Find which of the employees has the larger pay
increase and by how much.
The employee that has the larger pay increase is Jane. Her income is larger by £65.
Which employees has the larger pay increase?Percentage is the fraction out of an amount that is usually expressed as a number out of hundred.
Increase in Jane's salary = £14,000 x 0.018 = £252Increase in Lenny's salary = £11,000 x 0.017 = £187Difference in increase = $252 - £187 = £65To learn more about percentages, please check: https://brainly.com/question/25764815
#SPJ1
A jar contains five blue marbles, six red marbles, and four green marbles. What are the odds you will draw a blue marble from this jar?
Answer:
Probability=number of specific outcomes/total of all possible outcomes
There are 5 blue marbles and a total of 15 marbles.
So the probability of drawing a blue marble from the jar is:
5/15
1/3
Step-by-step explanation:
Hope this helps
Which lists the steps in the correct order to find the median of this data set? 24, 16, 23, 30, 18, 29 O 1. Put the numbers in order. 2. Cross off high/low pairs. 3. Add the leftover numbers. 4. Divide the sum by 2. O1. Put the numbers in order. 2. Cross of high/low pairs. 1. Cross off high/low pairs. 2. Add the leftover numbers. 3.Divide the sum by 2. 1. Cross of high/low pairs.
Median is the central tendency of the data and always exists in the middle of the data set.
What is the median?The Median is the middlemost value of the numbers arranged in the ascending orders. Median is the central tendency of the data and always exists in the middle of the data set.
The process of finding the median if the number of data points is even is as follows:
Put the numbers or the data points in the order(increasing or decreasing i.e. ascending or descending order)Next cross of the high/ low pairsAdd the leftover numbersand divide the number( as obtained in the above step by 2)( if the number of data pints were even then we just need to arrange the numbers and cross the high/low pair and only one data point will be left which acts as the Median of the data set)
To know more about median follow
https://brainly.com/question/26151333
#SPJ1
What is the value of the expression below?
2[3(16+)]-8
Answer:
94Step-by-step explanation
2 * [3 * (16 + 1)] - 8 =
2 * [3 * 17] - 8 =
2 * 51 - 8
102 - 8 =
94
Please help me with this one.
Answer:
V = 16W = 48Step-by-step explanation:
The triangles are congruent when corresponding sides are congruent.
__
ΔFGH ≅ ΔABC means corresponding sides are ...
(GH, BC) = (V, 16)
(HF, CA) = (48, W)
Corresponding sides being congruent means ...
V = 16
W = 48
please help me with this if you can? thanks alot :)))
The probabilities are:
P(red) = 5/24P(orange) = 0 P(blue) = 1/3P(not green)= 17/24P(green or black) = 11/24P(not yellow) = 1.How to find the probabilities?
The probability of getting a particular color of marble, is given by the quotient between the number of marbles of that color and the total number of marbles.
Here we have:
5 red marbles.7 green marbles.4 black marbles.8 blue marbles.So the total number is 5 + 7 + 4 + 8 = 24.
Then:
P(red) = 5/24P(orange) = 0/24 = 0 (because there are 0 orange marbles).P(blue) = 8/24 = 1/3P(not green) = (24 - 7)/24 = 17/24P(green or black) = (4 + 7)/24 = 11/24P(not yellow) = 24/24 = 1 (because there aren't yellow marbles).If you want to learn more about probability, you can read:
https://brainly.com/question/251701
#SPJ1