Answer:
1/4
Step-by-step explanation:
If you type cos(75)cos(15) into a scientific calculator, the answer comes out as 1/4.
The value of the trigonometric expression cos(75)cos(15) is 1/4 after applying the trigonometric identity.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have a trigonometric expression:
= cos(75°)cos(15°)
As we know the trigonometric identity:
cos(a)cos(b) = (1/2)[cos(a + b) + cos(a - b)]
a = 75
b = 15
Plug the above values in the trigonometric identity:
cos(75)cos(15) = (1/2)[cos(75 + 15) + cos(75 - 15)]
cos(75)cos(15) = (1/2)[cos(90) + cos(60)]
The trigonometric ratio is the ratio of the pair of a right-angled triangle.
The value of cos90 = 0
cos60 = 1/2
cos(75)cos(15) = (1/2)[0 + 1/2]
cos(75)cos(15) = 1/4
Thus, the value of the trigonometric expression cos(75)cos(15) is 1/4 after applying the trigonometric identity.
Learn more about trigonometry here:
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At the amusement park there were t-shirts for sale for $18.95 each. James bought 4 of them. About how much did he spend?
$80.00
$60.00
$24.00
$75.80
James would be spending the amount of $75.80 which is the correct answer would be an option (D).
What is the Multiplication operation?In mathematics, the multiplication operation Values on each side of the operator are multiplied.
We have been given that there were t-shirts for sale for $18.95 each at the amusement park, and James bought 4 of them.
To determine the amount of cost did he spend.
The amount of cost is equal to the multiplication of each t-shirts cost and
quantity.
The amount of cost = the cost of each t-shirt × quantity
The amount of cost = $18.95 × 4
Apply the multiplication operation to get
The amount of cost = $75.80
Therefore, he would be spending the amount of $75.80.
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A manufacturer claims that the mean lifetime of its lithium batteries is 1200 hours. A homeowner selects 25 of these batteries and finds the mean lifetime to be 1180 hours with a standard deviation of 80 hours. Test the manufacturer's claim. Use ΅ = 0.05. Round the test statistic to the nearest thousandth.
Answer:
Since p is > α we fail to reject the Null as the result is not significant at α = 0.05
Step-by-step explanation:
Given that:
Mean lifetime (m) = 1200
Sample size (n) = 25
Sample mean (x) = 1180
Standard deviation (s) = 80
α = 0.05
The null hypothesis :
H0 : m = 1200
Alternative hypothesis : m ≠1200
The t statistic :
(x - m) / (s/√n)
(1180 - 1200) / (80 / √25)
-20 / (80/5)
= - 1.250
P value = 0.10565 ( p value calculator)
Reject Null hypothesis if p > α
At α = 0.05
Since p is > α we fail to reject the Null as the result is not significant at α = 0.05
Andre and Elena knew that after 28 days they would have 2²⁸ coins, but they wanted to find out how many coins that actually is. Andre wrote: 2 28 = 56. Elena said, "No, exponents mean repeated multiplication. It should be 28 28, which works out to be 784." Do you agree with either of them? Explain your reasoning.
Answer:
I agree with none of them
Step-by-step explanation:
Given
[tex]Expression= 2^{28}[/tex]
[tex]Andre: 2 * 28 = 56[/tex]
[tex]Elena: 28 * 28 = 756[/tex]
Required
Who is correct?
[tex]Expression= 2^{28}[/tex]
When we apply law of indices to the above, it gives 2 multiplies by itself in 28 places
i.e.
[tex]Expression= 2^{28}[/tex]
[tex]Expression= 2*2*2*..........*2[/tex] ---- in 28 places
Andre's interpretation of the expression is incorrect as:
[tex]2^{28} \neq 56[/tex]
Also, Elena's expression is incorrect.
This is so, because
[tex]2^28 \neq 28*28[/tex]
Hence, both of them are incorrect and I agree with none of them
Write the inequality graphed below. Use "x" as your variable
Answer:
x is greater than or equal to 3. x > 3
Step-by-step explanation:
I forgot how to simplify like this can someone explain to me how i do this?
Answer:
Just subtract 11 from 7.
Answer:
-4
Step-by-step explanation:
Ryan and Sarah collect baseball cards. Ryan has 150 baseball cards and collects 10 cards per week. Sarah has 200 baseball cards and collects 5 cards per week. After how many weeks will Ryan and Sarah have the same number of cards?
Answer:
i need help on this question too
Step-by-step explanation:
Answer:
I think X=10 but im not for sure.
Step-by-step explanation:
150 (X+10) = 200 (X+5)
150x+1500 200X+1000
-150X -150X
1500 50X+1000
-1000 -1000
500 50X
50 50
10=X
(-3,7), (3,3) write in standard form
Answer:
3x−y=2
Step-by-step explanation:
PLEASE HELP
Write equations of the horizontal and vertical lines that pass through the given
point.
12. (-3,-4)
Horizontal line:
Vertical line:
Answer:
horizontal line: y=-4
vertical line: x=-3
Step-by-step explanation:
This one is simple. all you need to do is look at the x and y in the ordered pair.
Horizontal goes left and right so it's for y
Vertical goes up and down so it's for x
let me know if you need more explaining :)
What is the binary number for 16
Step-by-step explanation:
Answer:
0001 0000
this is the answer and i had to make it longer so i could post it
sorry if this is your second time answering or seeing this but my ads arent loading.
forty five children attend a preschool the number of two year olds is one half the number of three year olds the number of four year olds is the same as the number of three year olds
how many two year olds attend
how many three year olds attend
how many four year olds attend
Answer:
a=9
b=18
c=18
18+18+9=45 total children
plsssssssssssssss help with 11
Answer:
1 = $3.50
( I tried my best)
What is the absolute value of -250?
Answer:
250
Step-by-step explanation:
Pretty much every time it asks for the abasloute value it just asks how much to get the zero on the number line. It will ALWAYS be positive. For example -5 will be 5 to get to zero on the numberline. Same thing with a positive 5.
Please help me out with this picture.(#3a, #3b, and #3c)
Answer:
all are in the picture I attached
Step-by-step explanation:
hope this helps
3. A student wrote a book which she plans to sell online for $13 per copy. Her total expenses were $85. Which function can be used to find the profit in dollars, d, when the student sells C, copies of the book?
Answer:
Her profit in dollars is;
d = 13c - 85
Step-by-step explanation:
Mathematically,
profit = sales - cost price
She sells at $13 per copy
so for c copies, total sales amount will be 13 * c= $13c
So the profit d in dollars will be;
d = 13c - 85
What is the slope of the line passing through the points (-6, 33) and (-2, 15)?
Please answer quick
Answer:
The slope is -9/2
Step-by-step explanation:
m=y²-y¹/x²-x¹
m=15-33/(-2)-(-6)
m=-18/4
m=-9/2
I need help plz asap
================================================
Explanation:
Check out the diagram below.
Segment BD cuts angle EBC in half
So the two smaller pieces DBC and DBE are congruent. Let's call them x.
Let's make y = angle EBA.
Note how the diagram shows the angles x, x, and y forming a straight angle. So we can say
x+x+y = 180
2x+y = 180
y = -2x+180
We'll use this later.
For now, focus on triangle DEB. Angle E is 90 degrees and angle B is x.
D+E+B = 180
28+90+x = 180
x+118 = 180
x = 180-118
x = 62
Which means
y = -2x+180
y = -2*62+180
y = -124+180
y = 56
Now focus on triangle BEA. We have B = 56, E = 90 and A = z
B+E+A = 180
56+90+z = 180
146+z = 180
z = 180-146
z = 34
which is the measure of angle A.
[6×(4−2)+(21×23+1)]÷32
Answer:
Step-by-step explanation:
15.5
Answer:
15.5 is your answer. can I solve. for these u say yes or no
Sum of Angles
Find the value of x and the measure of every angle.
It is Geometry
10. At a certain company, the average starting salary s for a new worker is $25,000. The actual
salary has an absolute deviation of at most $1800. Write and solve an inequality to find the
range of the starting salaries.
Copyright © Big Ideas Learning, LLC
Integrated Mathematics 1
57
Answer:
Step-by-step explanation:
Let 'x' represent the actual salary.
|x - 25,000| <= 1800
- 1,800 <= x - 25,000 <= 1,800
25,000 - 1,800 <= x <= 25,000 + 1,800
23,200 <= x <= 26,800
The range of the salary is the closed interval [23,200, 26,800].
With a two-year agreement, Sarah can add up to 4 lines for $9.99 each. Her first monthly bill totals 89.96. Sarah did not exceed the "anytime minutes" limit and did not engage in "text messaging". How many lines did she add to her plan? Write an equation, and then solve.
Answer:
The answer is 267.
Step-by-step explanation:
If we wanted to represent this scenario as an equation, it would be 22.40-14+.5x (x being the amount of texts after 250). We are using PEMDAS, but because the variable is unknown, we skip multiplication and just go left to right. 22.40 - 14 = 8.40. With 8.40, we now know how much it costed AFTER 250 messages (how much she owes after $14). If we want to find how many PER 50 cents, we have to DIVIDE (reverse of multiplication). 8.4 / .5 = 16.80. Because you can't send .8 of a text message, you round to get 17. 250 + 17 = 267 (messages sent that month).
Therefore the answer is 267 (250 + 17)
How do you solve (3×-2)^3
Answer:
the answer should be -216
5)A plumber charges $25 for a service call plus $50 per hour of service. Write an equation in slope-intercept form for the cost, C, after h hours of service.
Answer: your Answer is $75 dollars.
Step-by-step explanation:
$25 + $50 = $75
Answer:
[tex]C = 50x + 25[/tex]
Step-by-step explanation:
The $50 charge can be interpreted as the slope, as it varies based on the amount of time the service takes. The $25 can be interpreted as the y-intercept, as you'll get charged $25 no matter how long the service takes. Thus, we can plug these values into the slope-intercept form equation.
[tex]y = mx + b\\C = 50x + 25[/tex]
The coordinates of three vertices of a square are (1, –1), (6, –1), and (6, 4). Fill in each blank to make the statement true. What is the area of the square?
Answer:
25units²Step-by-step explanation:
Given the coordinates of three vertices of a square as A(1, –1), B(6, –1), and C(6, 4). The area of the square is expressed as;
A = L² where;
L is the one of the side length of the square.
Note that all the sides of a square are equal;
To get one of the side length, we will find the distance between any two of the coordinates points. Using the coordinates A(1, –1), B(6, –1)
L = AB = √(x2-x1)²+(y2-y1)²
L = √(6-1)²+(-1-(-1))²
L = √5²+0²
L = √25
L = 5
Area of the square = 5²
Area of the square = 25units²
Hence the area of the square is 25units²
The price of an item yesterday was $180. Today, the price rose to $279. Find the percentage increase.
HELPPP
PLEASSE
DONT SWIPE PAST:,(
I SAW THATTTT
Answer: 55%
1. 279 - 180 = 99
2. 99 divided by 180 = 0.55
3. 0.55 x 100 is 55.
55 is the percentage
The average distance from the sun to the planet Venus is about 108,000,000 km. The diameter of a human hair is about 0.0025 mm.
(a) What is the distance from the sun to Venus written in scientific notation?
• [Please make sure to include your units]
(b) What is the diameter of a human hair written in scientific notation?
• [Please make sure to include your units]
(c) In comparing the measurements in Parts (a) and (b), what else must be done before a comparison is made?
Step-by-step explanation:
It is given that,
The average distance from the sun to the planet Venus is about 108,000,000 km. The diameter of a human hair is about 0.0025 mm.
(a) In scientifc notation, the distance from the Sun to Venus will be :
There are 8 numbers before 1. It means
d = 1.08 × 10⁸ km
(b) In scientific notation, the diameter of a human hair will be :
There are 3 numbers after decimal. It means
D = 2.5× 10⁻³ mm
(c) Before comparing two measurements, both values must be converted into the same units.
Since, 1 mm = 10⁻⁶ km
D = 2.5× 10⁻³ × 10⁻⁶ km
= 2.5 × 10⁻⁹ km
For comparison divide the distance from the Sun to Venus and the diameter of a human hair.
[tex]C=\dfrac{1.08\times 10^8\ km}{2.5\times 10^{-9}\ km}\\\\=4.32\times 10^{16}[/tex]
Hence, this is the required solution.
One of these graphs is of a cubic function which one is it ?
please helpp help I will be grounded if I don't get all of my answers. I will give brainleist
Answer:
D is the answer
Step-by-step explanation:
:)
5x + 2y = 9
-6x - 2y = -14
Answer:
What are you suppose to be finding? I am confused finding the value of x??
Step-by-step explanation:
What is the length of the unknown side?
Answer:
20！
Step-by-step explanation:
"Shaquille, Lyle, and Amanda collect stamps. Shaquille has one-half the number of stamps that Lyle has. Amanda has two-thirds as many stamps as Lyle. Together they have 364 stamps. How many stamps does Amanda own?" Please help me :c
Answer:
112 stamps
Step-by-step explanation:
Shaquille and Amanda's stamps are described in terms of Lyle's, so:
Lyle's = 6x 6x+3x+2x=364
Shaquille's = 3x 13x=364
Amanda's = 4x x=28
Lyle has 168 stamps, Shaquille has 84, and Amanda has 112. 168+84+112=364
A number times 7 is at least the number plus 6.6.
Write the inequality.
Answer:
7x ≥ x + 6
A number signifies x.
Replace "a number" with x and then write out the inequality.