To find the value of x and according to the given information, it is necessary to use cosine, which is the ratio between the adjacent side and the hypotenuse.
In this case the given angle is 43, it means that cos 43 is the ratio between 36 (adjacent side) and x (hypotenuse). Solve for x, this way:
[tex]\begin{gathered} \sin 43=\frac{36}{x} \\ x=\frac{36}{\sin 43} \\ x=52.8 \end{gathered}[/tex]x has a value of 52.8 (approximately).
A die is rolled 200 times with the following results. Outcome 1 2 3 4 5 6 Frequency 32 36 44 20 30 38 What is the experimental probability of rolling the given result? a number more than 3
The experimental probability of rolling such that the number is more than 3 is 0.44.
The proportion of outcomes where a specific event occurs in all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.
When a dies is rolled 200 times, the results are:
Frequency Outcome
1 32
2 36
3 44
4 20
5 30
6 38
Therefore,
The experimental probability that a number is more than 3 after rolling will be:
= The sum of outcome above 3 / total outcome
= ( 20 + 30 + 38 ) / ( 32 + 36 + 44 + 20 + 30 + 38 )
= 88/ 200
= 0.44
Hence, the probability that the number is more than 3 is 0.44.
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True or false: 8 is an integer
The answer is true
the number 8 is a whole number
so
is an integer
a number that can be written without a fractional component is an integer
A natural number is an integer greater than 0
help meee pleasee!!!
thank you <3
Answer:
y = -800x + 294000
286,000
Step-by-step explanation:
To write the equation, you need the slope and the y-intercept.
The slope is -800
You find the slope by the change in y over the change in x
[tex]\frac{288400 - 294000}{7 - 0}[/tex] = [tex]\frac{15600}{7}[/tex] = -800
Now we will find the y -intercept. I will use the slope and the point (0, 294,000) to find this. I could have used the other point given. They will both work.
slope (m) = -800
x = 0
y = 294000
y = mx + b
294000 = -800(0) = b
294000 = b
The equation is
y = mx + b
y = -800x + 294000
2014
y = -800x + 294000
y = -800(10) + 294000
y =-8000 + 294000
y = 286,000
please help me I am confused
The mass of a human cell In scientific notation is 1X 10^10 kg.
What is Scientific notation?
Scientific notation is a means to express values that are either too big or too little to be conveniently stated in decimal form (typically would lead to a long string of digits). It is also known as the standard form in the UK and scientific form, standard index form, and standard form. Scientists, mathematicians, and especially engineers frequently utilize this base ten notation because it can make some mathematical operations simpler.In many professions, huge numbers are typically expressed using the normalized scientific form, unless an alternative normalization method, such as engineering notation, is preferred.Given that mass of a human cell= is 0.000000000001 kg
In scientific notation = 1X 10^10 kg
The mass of a human cell In scientific notation is 1X 10^10 kg.
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What will be the new position of the given point (3, –5) after reflection across the y-axis?
which graph represents the solution to the system of linear inequalities x>3 and y < or equal to 2
EXPLANATION
The system that represents the solutions to x>3 and y≤ 2 is the OPTION A
Find the sum of a number 2 units to the left of 16?
2 units left of 16 is 14
The sum is:
16 + (-2) = 16 - 2 = 14
A square has a side of length 1.6 yards. What is the area of the square inches? Round to the nearest tenth
Given that the side of the square is 1.6 yards.
The area of the square is
[tex]A=a^2[/tex]Substitute a=1.6, we get
[tex]A=1.6^2=2.56yards^2[/tex]We need to convert yards to inches.
We know that
[tex]1\text{ yard =36 inches}[/tex]Taking square on both sides, we get
[tex]1^2yard^2=36^2inches^2[/tex][tex]1yard^2=1296inches^2[/tex]Multiplying by 2.56 on both sides, we get
[tex]1\times2.56yard^2=1296\times2.56inches^2[/tex][tex]2.56yards^2=3317.76inches^2[/tex]Rounding to the nearest tenth, we get
[tex]2.56yards^2=3317.8inches^2[/tex]Hence the area of the given square is 3317.8 square inches.
The perimeter of a square I must be greater than 102 inches but less than 138 inches find the range of the possible side lengths that satisfy these conditions hit the perimeter of the square is given by P equals 4S or S represent the length of the side explain your answer in interval notation used decimal forms for numerical value
The Solution:
Given:
[tex]\begin{gathered} 102We are required to find the range of a side (s).
[tex]102<4s\text{ or }4s<138[/tex]So,
[tex]\begin{gathered} 102<4s \\ \\ 4s>102 \\ \\ s>\frac{102}{4} \\ \\ s>\frac{51}{2} \\ \\ s>25.5 \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} 4s<138 \\ \\ s<\frac{138}{4} \\ \\ s<\frac{69}{2} \\ \\ s<34.5 \end{gathered}[/tex]Therefore, the correct answer is (25.5, 34.5)
Determine whether the graph represents a function.
Jim's gas tank is 1/3 full. After he buys 9 gallons of gas it is 5/6 full. How many gallons can Jim's tank hold?
tank is 1/3 full
after he buys 9 gallons of gas it is 5/6
How many gallons can Jim's tank hold?
[tex]\frac{5}{6}-\frac{1}{3}=\frac{1}{2}[/tex]9 gallons = 1/2 tank
18 gallons is the capacity of the tank
If they had 15 oranges,9 peaches and 18 pears to distribute into the baskets.How many baskets can they make with the SAME number of pieces of fruit in each one?? How many pieces of each type of fruit will be in each basket?
Write 0.0000215 in scientific notation.
Given:
The number is:
[tex]=0.0000215[/tex]Find-:
The scientific notation
Explanation-:
The scientific notation is:
[tex]\begin{gathered} =0.0000215 \\ \\ =\frac{0.0000215}{10000000} \end{gathered}[/tex]So, the scientific notation is:
[tex]\begin{gathered} =\frac{0.0000215}{10000000} \\ \\ =215\times10^{-7} \end{gathered}[/tex]An employer pays $450 towards health insurance, while the employer pays $475. what is the ratio of employers contributions to the employees contributions?
Given :
An employee pays $450 towards health insurance
The second employer pays $475.
So, the ratio of employers contributions to the employees contributions=
[tex]475\colon450=\frac{475}{450}=19\colon18[/tex]
Thirteen million, three hundred and two thousand, six hundred and forty? In numbers
33,300 is standard form of the given question .
What does basic math standard form mean?
Writing down extremely large or extremely small numbers simply is possible using standard form. 103 = 1000, so 4 × 103 = 4000 . Therefore, 4000 can be expressed as 4 103. Even bigger numbers can be easily recorded in standard form using this method. The conventional form of small numbers is also an option.Definition of Standard Form?
A standard form is a way of expressing a certain mathematical idea, such as an equation, number, or expression, in a way that adheres to a set of norms. The standard form is used to concisely represent very big or very small values. For instance, 4,500,000,000 years is how 4.5 billion years is written.Thirteen million, three hundred = 33,300
Two thousand, six hundred and forty = 2640
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polynomials: adding and subtracting polynomials find each sum or differenceplease do minimum steps
Question 5(Multiple Choice Worth 5 points)
(08.02 MC)
Which of the following tables shows the correct steps to transform x2 + 10x + 24 = 0 Into the form (x-p)² = q?
Ip and q are integers]
Step 1 x²+ 10x + 24-1-0-1
Step 2
x2²+ 10x+23 = -1
Step 3 (x + 5)2 =-1
Step 1 x²+ 10x+24-2-0-2
Step 2 x²+ 10x+22=-2
Step 3 (x+5)2 = -2
O
Step 1 x²+ 10x+24+2=0+2
Step 2
x²+ 10x + 26 = 2
Step 3
(x + 5)2 = 2
Step 1 x²+ 10x + 24 + 1 = 0+1
Step 2 x²+ 10x + 25 = 1
Step 3 (x + 5)2 = 1
3
The correct steps to transform x² + 10x + 24 = 0 into the form (x − p)² = q is a.
Step 1 x² + 10x + 24 − 1 = 0 − 1
Step 2 x² + 10x + 23 = −1
Step 3 (x + 5)² = −1 and
d.
Step 1 x² + 10x + 24 + 1 = 0 + 1
Step 2 x² + 10x + 25 = 1
Step 3 (x + 5)² = 1
What is meant by factorization?Factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.
a² + b² + 2ab = (a + b)²
Given: x² + 10x + 24 = 0
= x² + 2x × 5 + 24
so b² has to equal 25 = 5²
Now, x² + 10x + 24 = 0
x² + 2x × 5 + 24 + 1 = 0 + 1
simplifying the above equation, we get
x² + 2x × 5 + 25 = 1
(x + 5)² = 1
Therefore, the correct answer is option
a.
Step 1 x² + 10x + 24 − 1 = 0 − 1
Step 2 x² + 10x + 23 = −1
Step 3 (x + 5)² = −1 and
d.
Step 1 x² + 10x + 24 + 1 = 0 + 1
Step 2 x² + 10x + 25 = 1
Step 3 (x + 5)² = 1
The complete question is:
Which of the following tables shows the correct steps to transform x² + 10x + 24 = 0 into the form (x − p)² = q?[p and q are integers] (5 points)
Select one:
a.
Step 1 x² + 10x + 24 − 1 = 0 − 1
Step 2 x² + 10x + 23 = −1
Step 3 (x + 5)² = −1
b.
Step 1 x² + 10x + 24 − 2 = 0 − 2
Step 2 x² + 10x + 22 = −2
Step 3 (x + 5)² = −2
c.
Step 1 x² + 10x + 24 + 2 = 0 + 2
Step 2 x² + 10x + 26 = 2
Step 3 (x + 5)² = 2
d.
Step 1 x² + 10x + 24 + 1 = 0 + 1
Step 2 x² + 10x + 25 = 1
Step 3 (x + 5)² = 1
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help me please
thank you
Answer:
Domain: [1, 7]
Range: [-4, 2]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
WILL GIVE BRAINLYEST AND 30 POINTS ANSWER ASAP
5.2187 x 10^−3, 2.05 x 10^7, and 3.40 x 10^3 are multiplied. How many significant digits should the product have?
5
3
2
1
5.2187 x 10^−3, 2.05 x 10^7, and 3.40 x 10^3 multiply all the terms. There will be 9 significant digits in the final result.
Given that,
5.2187 x 10^−3, 2.05 x 10^7, and 3.40 x 10^3 multiply all the terms.
We have to find how many digits should be significant for the product.
Multiplication is the action of adding a number to itself for the specified number of times. For instance, 3 × 4 denotes the addition of 3 to itself 4 times, and the opposite is true for the other number.
The multiplication of the given numbers is
=5.1287 × 10⁻³ × 2.05 × 10⁷ × 3.40 × 10³
=5.1287 × 2.05 × 3.40 × 10⁽⁻³⁺⁷⁺³⁾
= 35.747039 × 10⁽⁻³⁺⁷⁺³⁾
= 35.747039 × 10⁷
= 3.5747 × 10⁸
Given that the digit "3" comes before the decimal and the number "10" has a power of 8. As a result, there are 9 significant digits in total (8 + 1).
Therefore, There will be 9 significant digits in the final result.
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Jill Has twenty carrots she sets some on display now she has two how many did she put on display?
Answer:
the answer is 18 because if Jill put 18 on display she would have 2 left
a jar contains 100 tickets for a drawing. Among those tickets are 7 winning tickets. what are the odds in favor of winning 7:937:10093:793:100
From the statement, we know that:
• a jar contains 100 tickets for a drawing,
,• among those tickets are 7 winning tickets.
We must find the odds in favour of winning.
The odds in favour of winning are:
Odds in favour = Number of successes : Number of failures
In this case, we have:
• Number of successes = 7,
,• Number of failures = 100 - 7 = 93.
So we have:
[tex]\text{ Odds in favour }=7:93.[/tex]Answer7:93
Help with this personal finance problem
Answer: Take home pay
75.49%
$1,283.39
Step-by-step explanation:
Gross pay
$1,700.00
ChevronIncome taxes
10.95%
$186.09
Federal Income Tax
12%
$123.27
Iowa State Tax
6.25%
$62.82
ChevronFICA taxes
7.16%
$121.72
Social Security
5.8%
$98.65
Medicare
1.36%
$23.07
ChevronPre-tax
6.4%
$108.80
Commuter Parking
6.4%
$108.80
Post-tax
0%
$0.00
Take home pay
75.49%
$1,283.39
Erica and Naomi are both pledging study hours as they prepare for theirAlgebra 1 EOC next week. Erica says that she is going to study fifteen minutesthe first night of this week and then double how much she studies every dayfor the next seven days. Naomi says she is going to study 3 hours the first daythis week and then is going to add on thirty minutes each day for the nextseven days.Part A: Write a recursive and explicit formula for each girl’s study pledge. Erica:Naomi:
we know that
Erica
The sequence in minute is
15,30,60,120,240,480,960
This is a geometric sequence
where
r=30/15=2 ----> common ratio
the recursive formula For n>1 is equal to
[tex]\begin{gathered} a_n=a_{(n-1)}*r \\ a_n=a_{(n-1)}*2 \end{gathered}[/tex]Find out the explicit formula
[tex]a_n=a_1*r^{(n-1)}[/tex]where
a1=15
r=2
[tex]a_n=15*2^{(n-1)}\text{ ----> explicit formula}[/tex]Naomi
we have the sequence in hours
3 3.5 4 4.5 5 5.5 6
This is an arithmetic sequence
where
d=3.5-3=0.5 ----> the common difference
the recursive formula For n> 1 is equal to
[tex]\begin{gathered} a_n=a_{(n-1)}+d \\ a_n=a_{(n-1)}+0.5 \end{gathered}[/tex]Find out the explicit formula
[tex]a_n=a_1+d(n-1)[/tex]where
a1=3
d=0.5
substitute
[tex]\begin{gathered} a_n=3+0.5(n-1) \\ a_n=3+0.5n-0.5 \\ a_n=0.5n+2.5\text{ ----> explicit formula} \end{gathered}[/tex]A bag of marbles contains 6 blue glass marbles, 5 yellow glass marbles, 12 blue stone marbles, and 3 yellow stone marbles. What is the probability of selecting a marble and having that marble be either a blue marble or a stone marble? Express your answer as a decimal rounded to four decimal places. Probability
The probability of selecting or having a marble to be either a blue marble or a stone marble is 0.8076.
Given, a bag contains 6 blue glass marbles, 5 yellow glass marbles,
12 blue stone marbles and 3 yellow stone marbles.
Probability of selecting a marble and having that marble to be either blue marble or a stone marble = ?
we know that,
Glass marbles:
n(B) = 6 and n(Y)= 5
Stone marbles:
n(B) = 12 and n(Y) = 3
Probability = Number of favorable outcomes/Total number of outcomes.
Probability of selecting a marble and having that marble to be either blue marble or a stone marble:
total number of blue marbles = 18
total number of stone marbles = 15
total number of marbles in the bag = 26
⇒ 18+15-12/26
⇒ 33-12/26
⇒ 21/26
= 0.8076
Hence the probability of selecting a marble and having that marble be either a blue marble or a stone marble is 0.8076.
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three numbers have a sum of 180. the second number is 4 times the smallest number. the third number is 7 times the smallest number. what is the largest number?
Answer:
105
Step-by-step explanation:
Let x, y and z be the 3 numbers in the order first, second and third
x + y + z = 180
Second number y is 3 times the smallest number and third number z is 7 times the smallest number. So smallest number has to be x
so y = 4x
z = 7x
x + y + z = x + 4x + 7x = 180
12x = 180
x = 15
Largest number = 7 x 15 = 105
Considering the function
H(x) = -x + 6
which statement is true?
A. The output value of the function is 4 when the input value is -2
B. The output value of the function is 7 when the input value is 1
C. The output value of the function is 6 when the input value is x
D. The output value of the function is 8 when the input value is -2
The statement which is true is Option(D) The output value of the function is 8 when the input value is -2.
What do mathematical functions mean?An expression, rule, or regulation that establishes a relationship between one variable (the independent variable) and another variable (the dependent variable) is referred to as a function in mathematics.
Given function:
H(x) = -x + 6
In Option A, the input value is -2 so the output of the function will be,
H(x) = -x + 6 = -(-2) +6 = 2+ 6 = 8 ,which is not equal to the given output value 4.
Hence, the statement is false.
Similarly in Option B and C, the input values are 1 and x.
H(x) = -x + 6 = -1 +6 = 5 ≠ 7
H(x) = -x + 6 ≠ 6
The given output values are not equal to the output values calculated.
So both statements are false.
In Option D the input value is -2 and the output value is 8 which is a correct statement as calculated in Option A.
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Dina pours 16-ounce containers juice into a dispenser with a capacity of 960 ounces. The function y = 16x modeled this situation. What is the range of the function ?
The range of the function, y = 16x, is 60, where y is 960.
What is the range of a function?The range of the function, y = 16x, are the possible values that x can assume to meet the value of y.
Usually, the range of a function is the output value.
Since the value of y = 960, the range of the function will be 60 (960/16).
The capacity of the dispenser = 960 ounces
The capacity of the juice containers = 16 ounces
The function that models the situation is y = 16x
Where y = 960
x = 60 (960/16)
Thus, the implication is that the range of the function or the number of 16-ounce containers that can fill the dispenser with a capacity of 960 ounces is 60.
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13 of 13 Want an extra challenge? This screen is **optional**: 30° If you want more practice to really level up your Right Triangle Trig skills, see if you can solve for the missing sides of the Right Triangle pictured to the left. a You can enter your results and check your work in the table below 7 HINT: The side that is 7 units long is OPPOSITE the 30° angle. Length of Hypotenuse (c) Length of Other Leg (a) Did I Get Them Right?! ( Nope. Keep trying Reset
Looking at the triangle, the reference angle is 30 degrees. The hypotenuse of the triangle is c. The opposite side of the triangle is 7 and the adjacent side is a.
We would determine the hypotenuse, c by applying the sine trigonometric ratio which is expressed as
Sin# = opposite side/hypotenuse
Sin 30 = 7/c
cSin30 = 7
c = 7/Sin 30 = 7/0.5
c = 14
We would determine the adjacent side, a by applying the tangent trigonometric ratio which is expressed as
Tan# = opposite side/adjacent side
Tan 30 = 7/a
aTan30 = 7
a = 7/Tan 30 = 7/0.5774
c = 12.12
On a coordinate plane, how are the locations of the points (3, -7) and (-3, 7) related?
A sequence starts Give a rule that the sequence could follow.
Let's say "n" is the last denominator
A rule that the sequence could follow is
[tex]\frac{1}{2n}[/tex]With 2 as the first value of n, this means that the next term will be 1/2(2)=1/4 and so on.
The next 3 terms in the sequence will be
1/2(8)=1/16
1/2(16)=1/32
1/2(32)=1/64
