The angle -30 degrees is not a correct answer because it falls outside of the given interval [0, 360 degrees). The correct answer is theta = 210 degrees, which satisfies the equation sine theta = -1/2 over the interval. In the fourth quadrant, the angle whose sine is -1/2 should be in the third quadrant to satisfy the inequality sine theta <= 0.
Explanation:In solving the equation Σ theta = -1/2, the student is looking for the values of theta that satisfy the equation over the interval [0, 360 degrees). The value -30 degrees is not a correct answer because it falls outside of the given interval. To find the correct answer, we need to determine the values of theta that make sine of theta equal to -1/2.
To find an angle whose sine is -1/2, we can look at the unit circle. In the first and second quadrants, the sine function is positive, so we need to look in the third and fourth quadrants.In the third quadrant (180 to 270 degrees), the sine function is negative. The angle whose sine is -1/2 in this quadrant is theta = 210 degrees.In the fourth quadrant (270 to 360 degrees), the sine function is positive again. However, the angle whose sine is -1/2 should be in the third quadrant to satisfy the inequality sine theta <= 0. Therefore, -1/2 is not a valid value for sine theta in the fourth quadrant.Learn more about Solving Equations here:https://brainly.com/question/29050831
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a campground owner had 150 meters of fencing to enclose a rectangualr field adjacent to a river and also bisect that field into two equal halves. No fencing required with river. what are the dimesions of the largest area that can be enclosed
Answer:
Dimension of the Rectangle : 2W - 150 by W
Step-by-step explanation:
Given
Land Size = 150 metres
This land size represents the perimeter of the land
Let P = Perimeter
So, P = 150 m
To bisect the field into two equal halves means to divide length or width of the field into two equal halves
Let L = Length of the field
Let W = Width of the field
Assuming the length of the field is to be bisected., then the campground owner is left with 0.5L (i,e half of the length)
Perimeter of a rectangle is calculated by: 2(Length + Width)
P = 2(L + W) by substitution, becomes
150 = 2(0.5L + W) ----open bracket
150 = L + 2W ---- Male L the subject the formula
L = 2W - 150
The dimension of the largest area that can be enclosed id given by (L,W)
By substitution; the expression becomes
Dimension of the Rectangle : 2W - 150 by W
the wheels of a bicycle are 0.6 m in diameter. If I go around the bike block, each wheel will perform 346 full turns. What distance, to the tenth of a meter ready, that represents it
Answer:
The distance that represents it is 651.9 m.
Step-by-step explanation:
In order to calculate the distance that the wheel travelled we need to find the length of the circumference of the wheel. This is given by the following formula:
length = 2*pi*r = pi*d
Since the diameter of the wheel is 0.6 m we can find the length of the wheel that is:
length = 3.14*0.6 = 1.884 m
The wheel made 346 full turns, that means that the total distance is the number of turns multiplied by the length of the wheel.
distance = 346*1.884 = 651.9 m
The distance that represents it is 651.9 m.
The model represents the factorization of 2x2+5x+3.
What are the factors of the polynomial?
'O
tx
+X
(2x+3)(x+1)
(2x-3)(x-1)
(3x+2)(x+1)
(3x-2)(x-1)
AX
Answer:
(2x+3)(x+1)
Step-by-step explanation:
Porque si lo factorizas da ese resultado.
The factors of the polynomial are (2x + 3) and (x+1)
Factorizing quadratic expressionsGiven the quadratic equation expressed as:
2x^2+5x+3
We are to find the factors of the given quadratic function as shown:
2x^2+5x+3
2x^2+2x +3x +3
2x(x+1)+ 3(x+ 1)
(2x + 3)(x + 1)
Hence the factors of the polynomial are (2x + 3) and (x+1)
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Can you help me with this please
Step-by-step explanation:
This is a cube
Formula surface area of a cube = s2 × 6
Where s is one side
Square of 8 = 64
64 × 6 = 384
f(x) = 4x2 + 7x - 18
Find f(-9)
Answer:
f(-9)= 243
Step-by-step explanation:
f(x) = 4x²+7x -18
f(-9) = 4(-9)²+7(-9)-18
= 4(81) -63-18
= 324- 81
= 243
Answer:279
Step-by-step explanation:
Bc
There are 2 brown marbles, 3 black marbles, and 4 gold marbles in a bag. What is the probability of drawing 2 brown marbles if the first is replaced after it is drawn?
Answer:
.049 (2sf)
Step-by-step explanation:
[tex] \frac{2}{9} \times \frac{2}{9} = 0.4938[/tex]
Answer & explanation:
The correct answer is 4/81. The probability of each marble drawn being brown is 2/9 because there are two brown marbles in a bag of nine total marbles. So, the probability that both marbles drawn will be brown is 2/9 times 2/9 or 4/81!
What is the value of the soccer ball?
1. baseball + basketball = 240
2. tennisball + soccerball = 500
3. soccerball - basketball + tennisball = 455
4. baseball + tennisball = 215
Subtract 1 from 4
5. tennisball - basketball = -25
Rearrange 3
6. soccerball + tennisball - basketball = 455
Substitute 5 into 6
7. soccerball - 25 = 455
Solve
soccerball = 480
Using this number cube and spinner, which simulation would help you answer this question? Over the past 50 years, records for one northwest city show that snow fell on the first day of winter 16 of the time. If you choose a year at random, what are the chances that the first day of winter will be a snowy Monday?
Answer:
0.045714286
Step-by-step explanation:
The chance of it being snowy is 16/50, or 0.32. And the chance of that day being Monday out of 7 days over the week is 1/7, or 0.143. Then the chances that the first day of winter will be a snowy Monday is 0.32*0.143 = 0.045714286
Answer:
A- roll and spin 50 times. Roll on a 3 AND land on red
Step-by-step explanation:
A zoo has some new exhibits.
In a survey, 2400 zoo attendants are asked to choose their favorite.
The results are shown in the following table.
(a) find the percentage for each type of animal.
Answer:
Elephant 14%
Panda 18%
Tiger 29%
Bonobo 39%
Step-by-step explanation:
Divide each number by 2400 then multiply the answer by 100.
The percentage of elephants, pandas, tigers, and bonobos are 14%, 18%, 29%, and 39% respectively.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
The zoo has some new exhibits.
In a survey, 2400 zoo attendants are asked to choose their favorite.
From the table:
The total number of animals = 336 + 432 + 696 + 936 = 2400
Percentage of Elephant = (336/2400)x100 = 14%
Percentage of Panda = (432/2400)x100 = 18%
Percentage of Tiger = (696/2400)x100 = 29%
Percentage of Bonobo = (936/2400)x100 = 39%
Thus, the percentage of elephants, pandas, tigers, and bonobos are 14%, 18%, 29%, and 39% respectively.
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Make the x the subject of the formula y= 7x + 4
Answer:
[tex]y = 7x + 4 \\ y - 4 = 7x \\ \frac{y - 4}{7} = \frac{7x}{7} \\ x = \frac{y - 4}{7} [/tex]
hope this helps you....
Answer:
x = y-4
7
Step-by-step explanation:
y = 7x + 4
y- 4 = 7x
[tex]\frac{y-4}{7}[/tex] =x
I need help please?!!!
Answer: (3)/(4)(3x+8), x^(2)-4, 3^(2+)x, -5(x-3)
Step-by-step explanation: Those are the right answers, trust me, this took a while.
Have a good day, brainliest wouldn't be bad :)
s the interquartile range of this data?
6
8
9
20
Box-and whisker plot titled Number of Coins in Collection with five-number summary from left to right 7, 16, 30, 36, 38.
We have been given the 5-number summary of a box plot that represents Coins in Collection. The five-number summary from left to right is 7, 16, 30, 36, 38.
We are asked to find the inter-quartile range of the given data.
We know that interquartile range is difference of upper quartile and lower quartile.
We know that the 5-point summary represents the lower data point, lower quartile, median, upper quartile and upper data point respectively.
We can see from our given 5 point-summary that lower quartile is 16 and upper quartile is 36.
[tex]\text{Interquartile range}=\text{Upper quartile}-\text{Lower quartile}[/tex]
[tex]\text{Interquartile range}=36-16[/tex]
[tex]\text{Interquartile range}=20[/tex]
Therefore, the interquartile range of the given data is 20 and last option is the correct choice.
Answer:
here is my answers, it is just my test....
What is the value of the expression StartAbsoluteValue negative 7 EndAbsoluteValue + StartAbsoluteValue negative 4 EndAbsoluteValue?
Answer:
11
Step-by-step explanation:
|-7|+|-4|
-|-7|-|-4|
Answer 11
Answer:
11
Step-by-step explanation:
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In a lab, 180 cells are present at the beginning of an experiment. During the first 9 hours, the number of cells increased by 8% each hour. Write an exponential model giving the number of cells y present t hours after starting the experiment. Estimate the time when the number of cells is 360.
Answer:
The answer is 9 hours
Step-by-step explanation:
From the initial population of 180 cells, the number grows by 8% every hour for the first 9 hours.
This represents a increased population of 108% the previous population.
108% = 108/100 = 1.08
So the new population after n hours is
180 x 1.08^n
When population is 360
360 = 180 x 1.08^n
1.08^n = 2
Take log of both sides
n x Log1.08 = Log 2
n = Log 2/Log 1.08
n = 9
An angle measures 49.4° less than the measure of its complementary angle. What is the measure of each angle?
Answer:
40.6
Step-by-step explanation:
Pretty sure a complementary angle is 90 so 90-49.4=40.6
Find the solutions of the quadratic equation Choose 1 answer:
Answer:
B
Step-by-step explanation:
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Answer:
(x+3)(2x+7)
Step-by-step explanation:
Step 1 :
Equation at the end of step 1 :
(2x2 + 13x) + 21
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 2x2+13x+21
The first term is, 2x2 its coefficient is 2 .
The middle term is, +13x its coefficient is 13 .
The last term, "the constant", is +21
Step-1 : Multiply the coefficient of the first term by the constant 2 • 21 = 42
Step-2 : Find two factors of 42 whose sum equals the coefficient of the middle term, which is 13 .
-42 + -1 = -43
-21 + -2 = -23
-14 + -3 = -17
-7 + -6 = -13
-6 + -7 = -13
-3 + -14 = -17
-2 + -21 = -23
-1 + -42 = -43
1 + 42 = 43
2 + 21 = 23
3 + 14 = 17
6 + 7 = 13 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 6 and 7
2x2 + 6x + 7x + 21
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (x+3)
Add up the last 2 terms, pulling out common factors :
7 • (x+3)
Step-5 : Add up the four terms of step 4 :
(2x+7) • (x+3)
Which is the desired factorization
Final result :
(x + 3) • (2x + 7)
- If you want this explained differently please let me know. Hope this helps!
Which value of x makes the equation true?
x + 7 = -9
Answer:
x = -16
Step-by-step explanation:
x + 7 = -9
x = -9 - 7
x = -16
Answer:
X=-16
Step-by-step explanation:
If you add -16 Then add a positive 7 you will end up with a -9
Have a great day
A 12 sided die with sides labeled 1 through 12 will be rolled once each number greater than 10?
Answer:
See the explaination
Step-by-step explanation:
Total No. of rolling each side of the 12-sided die= 12 x 12= 144 outcomes
No. of outcomes equals 10 are: (1, 9), (9, 1), (2, 8), (8, 2), (3, 7), (7, 3), (4, 6), (6, 4), (5, 5) = 9 outcomes.
No. of outcomes of rolling a No. >10: 144–9 = 135 outcomes.
Probability, Pr, of rolling a No. >10= 135/144
Pr (No. >10) = 0.9375 (to 4 dec. pl.)
Answer: I think you’re missing something on your question. But I think what your asking is how many numbers greater than 10. It should 2/12 or
Step-by-step explanation:
Write down the value of x = 65 give your reason for your answer
The cost of an entry ticket to an amusement park is $5 for a child and $8 for an
adult. During a given 15 minute period, 120 people entered the park, and the total
revenue from ticket sales was $810. During that 15 minute period, how many adults
entered the amusement park?
Answer:
70 adults
Step-by-step explanation:
because there is 70 adults and 50 kids
Solve the equation 2x2 + 13x + 15 = 0 by factoring. Show all steps.
Answer:
(2x + 3)(x + 5)
Step-by-step explanation:
2x² + 3x + 15 = 0
(2x + 3)(x + 5)
2x + 3 = 0
2x = -3
x = -3/2
x + 5 = 0
x = -5
Find four solutions of the equation. Write the solutions as ordered pairs.
y = x+5
Answer:
when x=1, y=6. etc.
Step-by-step explanation:
x y
1 6
2 7
3 8
4 9
Yolanda reads 24 chapters of a book in 6 hours. What is her rate in chapters per hour?
Answer:
4 chapters an hour
Step-by-step explanation:
24 / 6 = average of 4 chapters an hour
Answer:
4 chapters per hour
Step-by-step explanation:
[tex]rate \: of \: reading \\ = \frac{total \: chapters}{total \: time} \\ \\ = \frac{24}{6} \\ \\ = 4 \: chapters \: per \: hour[/tex]
Robert recently discovered a forgotten student loan bill. The amount due after 10 years is
now $10,819.33. He found some old statements and determined that after 7 years the bill
was $8831.80 and after 5 years he owed $7714.03.
1. How much did Robert borrow initially?
2. Robert is planning to pay the loan in full next year. How much will he owe then?
3. What is the interest rate on Robert’s loan?
Answer:
1.Robert borrowed $ 5,500.00
2.The amount Robert would repay next year is $ 11,576.69
3.The interest rate on the loan is 7%
Step-by-step explanation:
The interest on the loan can be computed using compound annual growth
rate
CAGR=(EB/BB)^1/n-1
EB is ending balance of $8831.80 in year7
BB is the balance of year 5 $7714.03
n=7-5=2
CAGR=(8831.8/7714.03)^(1/2)-1
CAGR==1.070000427-1
CAGR=0.070000427
CAGR=7%
The amount borrowed can be computed using the PV formula
At year 0 year 5 amount of $7714.03 is the future value
rate of interest is 7%
number of years is 5
PV=$7714.03*(1+7%)^-5
PV=$ 5,500.00
The amount Robert would pay next year is :
FV=$10,819.338(1+7%)^1
FV=$ 11,576.69
Select the correct answer.
In which direction must the graph of f(x) = 7* be shifted to produce the graph of g(x) = 7* + 7?
O A.
up
OB. right
0
C. down
0
D.
left
Reset
Next
Answer:
Maybe A hopefully its the correct answer
A soup can, shaped like a cylinder, has a diameter of 3.5 inches and a height of 5 inches. Each serving of soup is 15 cubic inches. If a can of soup this size costs $1.99, what is the cost of each serving of soup? Round to the nearest cent.
Answer:
The answer to your question is Cost of a serving = $0.62
Step-by-step explanation:
Data
diameter = 3.5 in
height = 5 in
each serving = 15 in³
Cost of the can = $1.99
Process
1.- Calculate the volume of the can
Volume = πr²h
-Substitution
Volume = (3.14)(3.5/2)²(5)
-Simplification
Volume = (3.14)(3.062)(5)
-Result
Volume = 48.08 in³
2.- Use proportions and cross multiplication to find the cost of a serving.
48.08 in³ ---------------- $1.99
15 in³ ---------------- x
x = (15 x 1.99)/48.08
x = 29.85/48.08
x = $0.62
Use these similar triangles on the coordinate plane to determine the equation of a straight line with a slope of 5/3 that passes through the origin.
y = five-thirds x
y = three-fifths x
y = 3x + 5
y = 5x + 3
Answer:
y = five-thirds x
Step-by-step explanation:
y = mx + b y intercept = 0
y = 5/3 x slope = 5/3
Answer:
The answer is A
Step-by-step explanation:
its easy pls like
Dave determines the meal he ordered at the restaurant contains 22% of his daily sodium intake. If the meal contains 260 mg of sodium, how many mg of sodium are in Dave's daily diet? Round your answer to the nearest whole mg
Answer:
1182 mg to the nearest mg.
Step-by-step explanation:
22% is equivalent to 260 mg sodium, so
100% is equivalent to 260 * (100/22)
= 1181.82 mg.
what is percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
Examples of percentages are:
10% is equal to 1/10 fraction
20% is equivalent to ⅕ fraction
25% is equivalent to ¼ fraction
50% is equivalent to ½ fraction
75% is equivalent to ¾ fraction
90% is equivalent to 9/10 fraction
Given,
Dave determines the meal he ordered at the restaurant contains 22% of his daily sodium intake
Meal contains 260 mg of sodium
22% is equivalent to 260 mg sodium, so
100% is equivalent to 260 x ([tex]\frac{100}{22}[/tex])
= 1181.82 mg.
22% is equivalent to 260 mg sodium, so
100% is equivalent to 260 * (100/22)
= 1181.82 mg.
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Calculate the simple interest on
N650.00 for 2 years at 6% per
annum.
Answer:
N78
Step-by-step explanation:
The explanation is in the picture
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