Answer:
a8= 23
Step-by-step explanation:
How do i write an akgebaric expression? Carrisa divided 40 grapes equally amoung f friends. How many grapes did each friend get?
How many friends?
40
____
X
40/ x
Jorge's hourly salary is $7.65. last week he worked 23 hour week how much did he earn
What does x equal
8=3+x/-6
A car is driving at a speed of 45mi/h. what is the speed of the car in feet per minute
In the week before and the week after a holiday there were 10,000 total deaths and 4968 of them occurred in the week before the holiday.
a) construct a 90% confidence interval estimate of the proportion of deaths in the week before the holiday to the total death in the week before and the week after the holiday
b) based on the result does there appear to be any indication that people can temporarily postpone their death to survive the holiday
The confidence interval is calculated based on the given values and can help determine if deaths are temporarily postponed during holidays.
Explanation:To construct a confidence interval estimate of the proportion of deaths in the week before the holiday to the total deaths in the week before and after the holiday, we can use the formula:
p ± z √(p(1- p/ n)
where p is the sample proportion, z is the z-score, and n is the sample size.
In this case, the sample proportion is p = 4968/10000 = 0.4968.
The z-score corresponding to a 90% confidence interval is approximately 1.645. The sample size is n = 10000.
Substituting these values into the formula, we get:
0.4968 ± 1.645 √((0.4968 * 0.5032) / 10000)
Calculating this expression gives us the confidence interval estimate.
Based on the result, we can assess whether there is an indication that people can temporarily postpone their death to survive the holiday. If the lower limit of the confidence interval is significantly lower than the proportion of deaths in the week after the holiday, it suggests that there is a decrease in deaths in the week before the holiday. However, if the lower limit is close to or higher than the proportion of deaths in the week after the holiday, it indicates that there is no evidence of a significant decrease in deaths before the holiday.
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25% of what number is 168.75
3x3 + 9x2 + x + 3 factor completely
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2". 1 more similar replacement(s).
3.1 3x3+9x2+x+3 is not a perfect cube
3.2 Factoring: 3x3+9x2+x+3
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: x+3
Group 2: 3x3+9x2
Pull out from each group separately :
Group 1: (x+3) • (1)
Group 2: (x+3) • (3x2)
-------------------
Add up the two groups :
(x+3) • (3x2+1)
Which is the desired factorization
3.3 Find roots (zeroes) of : F(x) = 3x2+1
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 3 and the Trailing Constant is 1.
The factor(s) are:
of the Leading Coefficient : 1,3
of the Trailing Constant : 1
Let us test ....
Polynomial Roots Calculator found no rational roots
Processing ends successfully
Angle θ lies in the second quadrant, and sin θ = 3/5.
cos θ =
tan θ =
Answer:
[tex]cos\Theta =\frac{4}{5}[/tex]
[tex]tan\Theta =\frac{3}{4}[/tex]
Step-by-step explanation:
Given : sin θ = 3/5
To Find : value of cos θ and tan θ
Solution :
use the identity:
[tex]sin^{2}\Theta +cos^{2}\Theta =1[/tex]
putting value of sin θ
⇒ [tex](\frac{3}{5})^{2} + cos^{2}\Theta =1[/tex]
⇒[tex]\frac{9}{25} +cos^{2}\Theta =1[/tex]
⇒[tex]cos^{2}\Theta = 1-\frac{9}{25}[/tex]
⇒[tex]cos^{2}\Theta = \frac{16}{25}[/tex]
⇒[tex]cos\Theta = \sqrt{\frac{16}{25}}[/tex]
⇒[tex]cos\Theta =\frac{4}{5}[/tex]
Thus , [tex]cos\Theta =\frac{4}{5}[/tex]
Now to find value of tan θ
Since we know that
⇒ [tex]tan\Theta =\frac{sin\Theta }{cos\Theta }[/tex] (identity)
⇒[tex]tan\Theta =\frac{\frac{3}{5} }{\frac{4}{5} }[/tex]
⇒[tex]tan\Theta =\frac{3}{5}\div \frac{4}{5}[/tex]
⇒[tex]tan\Theta =\frac{3}{5}\times \frac{5}{4}[/tex]
⇒[tex]tan\Theta =\frac{3}{4}[/tex]
Thus , the value of
[tex]tan\Theta =\frac{3}{4}[/tex]
[tex]cos\Theta =\frac{4}{5}[/tex]
Final answer:
This detailed answer provides the values of cos θ and tan θ for an angle θ in the second quadrant given sin θ = 3/5. It explains the process using the Pythagorean identity and the characteristics of the second quadrant.
Explanation:
cos θ = -4/5
tan θ = -3/4
Given sin θ = 3/5 and the angle θ lies in the second quadrant, we can determine cos θ using the Pythagorean identity. Since sin θ = 3/5 is positive in the second quadrant, the x-coordinate in the triangle would be negative. Therefore, cos θ = -4/5. Similarly, tan θ can be calculated as tan θ = sin θ / cos θ = (3/5) / (-4/5) = -3/4.
(only subject im bad at) What is the Least Common Denominator (LCD) of 7/8 and 1/6 ?
How much of the circle is shaded? Write your answer as a fraction in simplest form?
Answer:
[tex]5/14[/tex]
Step-by-step explanation:
Let
x-----> the shaded area
we know that
[tex]x+\frac{1}{7}=\frac{1}{2}[/tex]
solve for x
Multiply by [tex]14[/tex] both sides
[tex]14x+2=7[/tex]
[tex]14x=7-2[/tex]
[tex]14x=5[/tex]
Divide by [tex]14[/tex] both sides
[tex]x=5/14[/tex] ----> fraction irreducible
Express x in terms of the other variables in the diagram below:
From the diagram below , x = t ( r - h ) / h
Further explanationFirstly , let us learn about trigonometry in mathematics.
Suppose the ΔABC is a right triangle and ∠A is 90°.
sin ∠A = opposite / hypotenusecos ∠A = adjacent / hypotenusetan ∠A = opposite / adjacentThere are several trigonometric identities that need to be recalled, i.e.
[tex]cosec ~ A = \frac{1}{sin ~ A}[/tex]
[tex]sec ~ A = \frac{1}{cos ~ A}[/tex]
[tex]cot ~ A = \frac{1}{tan ~ A}[/tex]
[tex]tan ~ A = \frac{sin ~ A}{cos ~ A}[/tex]
Let us now tackle the problem!
Look at ΔADE in the attachment.
We will use the following formula to find relationship between variable t and h:
tan ∠A = opposite / adjacent
[tex]\tan \angle A = \frac{DE}{AD}[/tex]
[tex]\large {\boxed{ \tan \angle A = \frac{h}{t} } }[/tex] → Equation 1
Look at ΔABC in the attachment.
We will use the following formula to find relationship between variable r , t and x:
tan ∠A = opposite / adjacent
[tex]\tan \angle A = \frac{BC}{AB}[/tex]
[tex]\large {\boxed{ \tan \angle A = \frac{r}{x + t} } }[/tex] → Equation 2
Next we can substitute equation 1 to equation 2 :
[tex]\tan \angle A = \frac{r}{x+t}[/tex]
[tex]\frac{h}{t} = \frac{r}{x+t}[/tex]
[tex](x + t)h = r ~ t[/tex]
[tex](x + t) = \frac{(r ~ t)}{h}[/tex]
[tex]x = \frac{(r ~ t)}{h} - t[/tex]
[tex]x = \frac{(r ~ t)}{h} - \frac{(h ~ t)}{h}[/tex]
[tex]\large {\boxed {x = \frac{t(r - h)}{h}} }[/tex]
Learn moreCalculate Angle in Triangle : https://brainly.com/question/12438587Periodic Functions and Trigonometry : https://brainly.com/question/9718382Trigonometry Formula : https://brainly.com/question/12668178Answer detailsGrade: College
Subject: Mathematics
Chapter: Trigonometry
Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse , Triangle , Fraction , Lowest , Function , Angle
The end of a hose was resting on the ground, pointing up an angle. Sal measured the path of the water coming out of the hose and found that it could be modeled using the equation f(x) = –0.3x2 + 2x, where f(x) is the height of the path of the water above the ground, in feet, and x is the horizontal distance of the path of the water from the end of the hose, in feet.
When the water was 4 feet from the end of the hose, what was its height above the ground?
Answer:
3.2 feet
Step-by-step explanation:
The equation [tex]f(x)=-0.3x^{2}+2x[/tex] shows the height of water [[tex]f(x)[/tex]] and horizontal distance [[tex]x[/tex]].
Given the horizontal distance is 4 feet, they want to know the height.
Simply put 4 in [tex]x[/tex] of the equation and solve for [tex]f(x)[/tex]. So,
[tex]f(x)=-0.3(4)^{2}+2(4)\\f(x)=3.2[/tex]
So, the height of the water was 3.2 feet above the ground.
Manny has 48 feet of wood. He wants to use all of it to create a border around a garden. The equation 2l + 2w = 48 can be used to find the length and width of the garden, where l is the length and w is the width of the garden. If Manny makes the garden 15 feet long, how wide should the garden be? 9 feet 18 feet 30 feet 33 feet
Answer:
You can find a width of 9 feet.
Step-by-step explanation:
The width of the rectangular shaped garden should be 9 feet
What is the Perimeter of a Rectangle?The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.
Perimeter P of rectangle = 2 ( Length + Width )
Given data ,
Let the perimeter of the rectangle be P = 48 feet
We can use the equation given to solve for the width w of the garden:
2l + 2w = 48
Substituting l = 15, we get:
2(15) + 2w = 48
30 + 2w = 48
Subtracting 30 from both sides, we get:
2w = 18
Dividing both sides by 2, we get:
w = 9 feet
Hence , the width of the garden should be 9 feet
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which of the following represents the most accurate estimation of 96-38?
Prove:
lim x^3 = 8.
x approaches 2
Help Me Please???:):D
four years after a hedge maple tree was planted, its height was 9 feet. eight years after it was planted, the hedge maple tree's height was 12 feet. what is the growth rate of the hedge maple? what was its height when it was planted?? ...?
The growth rate of the hedge maple tree is 0.75 feet per year, and the tree's original height when it was planted was 6 feet.
Explanation:We are tasked with finding the growth rate of a hedge maple tree and its original height when it was planted based on the given data. The tree's height was recorded at two different times: Four years after it was planted, its height was 9 feet, and eight years after planting, its height reached 12 feet.
To calculate the growth rate per year, we take the difference in height over the difference in time:
Growth rate = (Height at 8 years - Height at 4 years) / (Time at 8 years - Time at 4 years)
Thus, Growth rate = (12 feet - 9 feet) / (8 years - 4 years) = 3 feet / 4 years = 0.75 feet per year.
To determine the original height when the tree was planted, we can subtract the total growth over the four years from the height at four years after planting:
Original height = Height at 4 years - (Growth rate * 4 years)
Original height = 9 feet - (0.75 feet/year * 4 years) = 6 feet.
if you drive your car constant speed of 45 miles per hour, how long will it take to travel 378 miles
A business purchased for $650,000 in 1994 is sold in 1997 for $850,000. What is the annual rate of return for this investment?
what is the coefficient of the term 13a in the expression 13a+6b
Answer:
The coefficient of the term 13a is, 13
Step-by-step explanation:
Coefficient term are the numbers that multiply the variables or letters
In the given expression: [tex]13a+6b[/tex]
13a means 13 times a , and a is the variable,
so 13 is the coefficient .
6b means 6 times b , and b is the variable ,
so 6 is the coefficient .
therefore, the coefficient of the term 13a in the given expression is, 13.
A distribution of numbers has the following five-number summary:
10.0, 15.0, 30.9, 50.0, 63.7
True or False? These numbers can be used to calculate the standard deviation of the distribution. ...?
Answer:
False
Step-by-step explanation:
A five number summary consists of these five statistics: the minimum value, the first quartile, the median, the third quartile, and the maximum value of a set of numbers
A standard deviation is a measure that is used to quantify the amount of variation or dispersion of a set of data values.
Std deviation is the square root of variance
Variance is the average of squares of deviations of each entry from the mean.
Hence from five point summary, we cannot calculated standard deviation of the distribution
The following is a correspondence one is
A.{(a,1),(b,1),(c,1)}
B.{(1,a),(2,c),(3,d)
C.{(1,b),(2,c),(3,b)
D.{(a,b),(c,d),(b,d)
Tommy has a pet monkey. Every day, his monkey eats 4 apples in the morning. The monkey also eats two bananas for every banana that Tommy eats.
Write an equation to describe this situation where x is the number of bananas Tommy eats and y is the total number of pieces of fruit the monkey eats.
Answer:
The required equation is : [tex]2x+4[/tex]
Step-by-step explanation:
Tommy's monkey eats 4 apples in the morning. The monkey also eats two bananas for every banana that Tommy eats.
Let Tommy eats x bananas, then the monkey eats 2x bananas.
Then, the required equation will be :
[tex]2x+4[/tex]
i need work shown write .569 as a percent
Which of the following represents the set of possible rational roots for the polynomial shown below?
x^3+5x^2-8x-20=0
A.{1/2, 1,2, 5/2, 4, 5, 10, 20}
B. {+/-1, +/-2, +/-4, +/-5, +/-10}
C. {+/-1/2, +/-1, +/-2, +/-5/2, +/-4, +/-5, +/-10, +/-20}
D. {+/-2/5, +/-1/2, +/-1, +/-2, +/-2/5, +/-1/5, +/-1/10} ...?
The set of possible rational roots for the polynomial is {±1, ±2, ±4, ±5, ±10, ±20}.
Thus, option (B) is correct.
Given:
[tex]x^3+5x^2-8x-20=0[/tex]
Using Rational Root Theorem
if a rational number p/q is a root of the polynomial, then p is a factor of the constant term, and q is a factor of the leading coefficient.
Here, p= -20 and q= 1.
So, the factors of -20 are:
-20, -10, -5, -4, -2, -1, 1, 2, 4, 5, 10, 20.
The factors of 1 (leading coefficient) are:
-1, 1.
Therefore, the possible rational roots are the combinations of these factors, where the numerator is a factor of -20, and the denominator is a factor of 1.
Combining the factors, the set of possible rational roots:
{±1, ±2, ±4, ±5, ±10, ±20}
Thus, option (B) is correct.
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What is the coefficient of the term 53xy ? A. 5 B.1/3 C.5xy D.5/3
Answer:
the answer is D, TRUST ME
Step-by-step explanation:
The coefficient of the term (5/3) x y is 5/3.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given expression is,
(5/3) x y
The coefficient of any expression is the numerical term,
Numerical term in the expression is 5/3.
So, the coefficient of the term (5/3) x y is 5/3.
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Find the equation of a circle in standard form where C(6, -2) and D(-4, 4) are endpoints of a diameter. ...?
Which of the following represents this function written in standard form?
y=2(x+1)(x-6)
a. y=3x^2-10x-12
b.y=2x^2-10x+6
c. y=2x^2-5x-12
d. y=2x^2-14x+12
Which of the following represents this function written in standard form?
y=2(x+1)(x-6)
a. y=3x^2-10x-12
b.y=2x^2-10x+6
c. y=2x^2-5x-12
d. y=2x^2-14x+12
Answer:
[tex]y=2x^2-10x-12[/tex]
Step-by-step explanation:
[tex]y=2(x+1)(x-6)[/tex]
write the given function in standard form
Standard form is [tex]y=ax^2+bx+c[/tex]
[tex]y=2(x+1)(x-6)[/tex] multiply the parenthesis using FOIL method
[tex]y=2(x^2-6x+1x-6)[/tex]
multiply 2 inside the parenthesis
[tex]y=2(x^2-6x+1x-6)[/tex]
[tex]y=2x^2-12x+2x-12[/tex]
Combiene like terms
[tex]y=2x^2-10x-12[/tex]
Which of the following expressions are equal to the one below?
(8+7) x 11
A. 8+ (7x11)
B. 11 x (8+7)
C. 8 x 11 - 7 x 11
D. 11 x 7 + 11 x 8
Use the quadratic formula to solve 9x2 + 6x – 17 = 0
The standard form of a quadratic equation is :
ax² + bx + c = 0
And the quadratic formula is:
[tex] x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} [/tex].
So, first step is to compare the given equation with the above equation to get the value of a, b and c.
So, a = 9, b = 6 and c = - 17.
Next step is to plug in these values in the above formula. Therefore,
[tex] x=\frac{-6\pm\sqrt{6^2-4*(9)*(-17)}}{2*9} [/tex]
[tex] =\frac{-6\pm\sqrt{36+612}}{18} [/tex]
[tex] =\frac{-6\pm\sqrt{648}}{18} [/tex]
[tex] =\frac{-6\pm\sqrt{324*2}}{18} [/tex]
[tex] =\frac{-6\pm\sqrt{324}*\sqrt{2}}{18} [/tex]
[tex] =\frac{-6\pm18*\sqrt{2}}{18} [/tex]
[tex] =-\frac{6}{18} \pm\frac{18\sqrt{2}}{18} [/tex]
[tex] =-\frac{1}{3} \pm\sqrt{2} [/tex].
So, x = [tex] -\frac{1}{3} \pm\sqrt{2} [/tex]
Answer: x= -1 + 3 sq root 2 /3
Step-by-step explanation:
the plus has a Line under it
Solve the problem. Susan purchased some municipal bonds yielding 7% annually and some certificates of deposit yielding 9% annually. If Susan's investment amounts to $19,000 and the annual income is $1590, how much money is invested in bonds and how much is invested in certificates of deposit? a. $13,500 in bonds; $5500 in certificates of deposit b. $5500 in bonds; $13,500 in certificates of deposit c. $13,000 in bonds; $6000 in certificates of deposit d. $6000 in bonds; $13,000 in certificates of deposit
...?
Susan invested $6,000 in municipal bonds and $13,000 in certificates of deposit. For the bond investment scenario, given the increase in market interest rate to 9%, you would pay less than $10,000 for the bond. The calculation shows you would be willing to pay approximately $9,724.77.
Explanation:To solve Susan's investment problem, we can set up a system of equations using the information provided in the problem. Let x be the amount invested in municipal bonds and y be the amount invested in certificates of deposit (CDs). We can then set up the following equations:
x + y = $19,000 (Total investment amount)
0.07x + 0.09y = $1,590 (Total annual income from investments)
Now, we solve the system of equations. Multiplying the second equation by 100 to get rid of decimals:
7x + 9y = 159,000
Next, we can multiply the first equation by 7 to help us eliminate one variable:
7x + 7y = 133,000
Subtracting the modified first equation from the second equation:
9y - 7y = 159,000 - 133,000
2y = 26,000
y = $13,000
Using y = $13,000 in the first equation:
x + 13,000 = 19,000
x = $6,000
Therefore, Susan invested $6,000 in municipal bonds and $13,000 in certificates of deposit.
Regarding the bond investment scenario:
a. Since the market interest rate has risen to 9%, higher than the bond's 6% interest rate, you would expect to pay less than $10,000 for the bond.
b. To calculate the price you would be willing to pay, you need to find the present value of the expected payment from the bond one year from now:
The expected payment is $10,000 (the face value) plus $600 (the final interest payment), which totals $10,600.
Using the market interest rate of 9%, the present value (PV) formula is:
PV = Payment / (1 + market interest rate)
PV = $10,600 / (1 + 0.09)
PV = $10,600 / 1.09
PV ≈ $9,724.77
Therefore, you would be willing to pay approximately $9,724.77 for the bond.