Answer:
a = -2
Step-by-step explanation:
f(x)=ax+b
f(2)=1
f(-3)=11
f(2) = 1 means 2a+b =1
f(-3)=11 means -3a + b = 11
Subtracting the two equations
-(-3a +b =11) becomes 3a -b = -11 so we can add
2a+b =1
3a - b = -11
----------------------
5a = -10
Divide by 5
5a/5 = -10/5
a=-2
The odds in favor of a horse winning a race are 7:4. Find the probability that the horse will win the race.
Answer:
7/11 = 0.6363...
Step-by-step explanation:
7 + 4 = 11
probability of winning: 7/11 = 0.6363...
The probability that the horse will in the race is [tex]\mathbf{\dfrac{7}{11}}[/tex]
Given that the odds of the horse winning the race is 7:4
Assuming the ratio is in form of a:b, the probability of winning the race can be computed as:
[tex]\mathbf{P(A) = \dfrac{a}{a+b}}[/tex]
From the given question;
The probability of the horse winning the race is:
[tex]\mathbf{P(A) = \dfrac{7}{7+4}}[/tex]
[tex]\mathbf{P(A) = \dfrac{7}{11}}[/tex]
Learn more about probability here:
https://brainly.com/question/11234923?referrer=searchResults
Find the function h(x) = f(x) - g(x) if f(x) = 3^x and g(x) = 3^2x - 3^x. A.h( x) = 0 B.h( x)=-3^2x C.h( x) = 3^x (2 - 3^x) D.h( x) = 2(3^2x)
Answer:
3^x( 2-3^x)
Step-by-step explanation:
f(x) = 3^x and g(x) = 3^2x - 3^x
h(x) = f(x) - g(x)
3^x - ( 3^2x - 3^x)
Distribute the minus sign
3^x - 3^2x + 3^x
2 * 3^x - 3 ^ 2x
Rewriting
We know that 3^2x = 3^x * 3^x
2 * 3^x - 3^x* 3^x
Factoring out 3^x
3^x( 2-3^x)
Vhat is the volume of the right rectangular prism?
Will mark brainliest
Answer:
432 mm³
Step-by-step explanation:
Volume of a Rectangular Prism: V = lwh
Step 1: Define variables
l = 8
w = 6
h = 9
Step 2: Plug into formula
V = 8(6)(9)
Step 3: Evaluate
V = 48(9)
V = 432
And we have our answer!
An animal population is increasing at a rate of 13 51t13 51t per year (where t is measured in years). By how much does the animal population increase between the fourth and tenth years.
Answer:
ΔP = 567
Step-by-step explanation:
The increasing rate of the population is 13,51*t.
That rate by definition is:
dP/dt where P is the population therefore
dP/dt = 13,51*t
dt = 13,51*t*dt
Integrating on both sides of the equation we get:
∫dp = ∫ 13,51*t*dt
P = 13,51*t²/2 + K ( K is population for t = 0 )
Now the population in 10 years P(₁₀)
P(₁₀) = 13,51* (10)² /2 + K
P(₁₀) = 675,5 + K (1)
And P(₄) is
P(₄) = 13,51*(4)²/2 * K
P(₄) = 108,08 + K (2)
Then substracting
P(₁₀) - P(₄) = ( 675,5 + K ) - ( 108,08 + K )
ΔP = 567,42
But we don´t have fraction of animal, then
ΔP = 567
Explain the difference between using the sine ratio to solve for a missing angle in a right triangle versus using the cosecant ratio. You must use complete sentences and any evidence needed (such as an example) to prove your point of view. (10 points)
Answer:
The sine ratio is the ratio between the opposite side over hypotenuse. The cosecant ratio is the ratio between the hypotenuse over the opposite side, therefore cosecant is the reciprocal of sine.
To find a missing angle using sine, you would need to use the inverse of sine. For example, if the sine was [tex]\frac{30}{40}[/tex], to find the angle you would need to find sin⁻¹ of [tex]\frac{30}{40}[/tex] which is x = sin⁻¹ (0.75). Therefore x equals approximately 49°.
A plane is flying at the height of 5000 meter above the sea level. at a particular point, it is excatly above a submarine floating 1200 meter below the sea level. what is the vertical distance between them ?
Answer:
3800 meters
Step-by-step explanation:
Helppppp thxxxxxxxxxx
Answer:
F. [tex] \frac{3}{2} [/tex]
Step-by-step explanation:
[tex] \frac{a + 2b}{b} = \frac{7}{2} [/tex]
Cross multiply:
7b= 2(a +2b)
Expand:
7b= 2a +4b
Bring all common variables to 1 side:
7b -4b= 2a
3b= 2a
divide by 2 on both sides:
[tex] \frac{3}{2} b = a[/tex]
divide by b on both sides:
[tex] \frac{3}{2} = \frac{a}{b} \\ \frac{a}{b} = \frac{3}{2} [/tex]
Define “constant value”
A fixed value. In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number. Example: in "x + 5 = 9", 5 and 9 are constants.
(a) Find the standard error of the mean for each sampling situation (assuming a normal population). (Round your answers to 2 decimal places.) (a) σ = 18, n = 9 (b) σ = 18, n = 36 (c) σ = 18, n = 144
Answer:
a) 6.00
b) 3.00
c) 1.50
Step-by-step explanation:
Sample error of the mean is expressed mathematically using the formula;
SE = σ /√n where;
σ is the standard deviation and n is the sample size.
a) Given σ = 18, n = 9
Standard error of the mean = σ /√n
Standard error of the mean = 18/√9
Standard error of the mean = 18/3
Standard error of the mean = 6.00
b) Given σ = 18, n = 36
Standard error of the mean = σ /√n
Standard error of the mean = 18/√36
Standard error of the mean = 18/6
Standard error of the mean = 3.00
c) Given σ = 18, n = 144
Standard error of the mean = σ /√n
Standard error of the mean = 18/√144
Standard error of the mean = 18/12
Standard error of the mean = 3/2
Standard error of the mean = 1.50
illustrate the distributive property to solve 144/8
Answer:
8 (19) or 8 (18 +1)
Step-by-step explanation:
Distributive property means to distribute.
HCF of 144 and 8.
=> 8 is the HCF of 144 and 8
8 (18 + 1)
=> 8 (19)
What is 28% of 58?
Hhhhhhh
Answer:
16.24
Step-by-step explanation:
of means multiply
28% * 58
Change to decimal form
.28 * 58
16.24
Answer:
[tex]\Large \boxed{\mathrm{16.24}}[/tex]
Step-by-step explanation:
[tex]28\% \times 58[/tex]
[tex]\displaystyle \sf Apply \ percentage \ rule : a\%=\frac{a}{100}[/tex]
[tex]\displaystyle \frac{28}{100} \times 58[/tex]
[tex]\sf Multiply.[/tex]
[tex]\displaystyle \frac{1624}{100} =16.24[/tex]
If 2 x 2 + 13 x − 7 = 0 , then x could equal which of the following?
Hi there! :)
Answer:
x = 1/2 or -7.
Step-by-step explanation:
(I'm assuming the expression is 2x² + 13x - 7 = 0)
Factor the equation to solve for the possible values of "x":
2x² + 13x - 7 = 0
When factored, we get:
(2x - 1) ( x + 7) = 0
Use the Zero-Product property to solve for the roots:
2x - 1 = 0
2x = 1
x = 1/2.
-----------
x + 7 = 0
x = -7.
Therefore, possible values of x are x = -1/2, 7.
Answer:
x = 1/2 x=-7
Step-by-step explanation:
2 x^2 + 13 x − 7 = 0
Factor
(2x-1)(x+7)=0
Using the zero product property
2x-1 =0 x+7=0
2x=1 x =-7
x = 1/2 x=-7
Suppose that a polynomial function of degree 4 with rational coefficients has 6, 4, 6i as zeros. Find the other zero
Answer:
-6i
Step-by-step explanation:
Complex roots have to come in conjugate pairs
So if we have 6i as a root, we must have -6i as a root
Answer:
-6i
Step-by-step explanation:
Hello, because this polynomial function has real coefficients and 6i is a zero, the conjugate of 6i is a zero as well. It means -6i is a zero.
The degree is 4 the number of zeroes is less or equal to 4 and we have already, 6, 4, 6i and -6i. So we have all the zeroes.
Thank you
Please help!! find the value of the expression
Answer:
7
Step-by-step explanation:
First plug in the variable amounts so the expression now looks like this:
(3 × 4 - 12) + 1/2(4 × 6 - 10)
Now, start by solving the multiplication parts first, so it now looks like this:
(12 - 12) + 1/2(24 - 10)
Now, apply the rules of order of operation, so start by solving what's in parenthesis. It should now look like this: (0) + 1/2(14)
Next, solve the multiplication part, so it now looks like this: 0 + 7
Solve that and the answer is 7.
A professor graded the final exams and found that the mean score was 70 points. Which of the following can you conclude?
A- All of the above.
B- The median score was 70 points.
C- 50% of the students scored below 70 points.
D- This would be a normal distribution.
Answer: C) 50% of the students scored below 70%
Step-by-step explanation:
Mean is the average. To find the mean (aka average) you add up all of the scores and divide by the number of tests.
B) The mean can be 70 without any test scoring 70% so B is not true.
A) Since B is not true, then A is not a valid option.
D) We don't know any of the other data so don't know if it is skewed left, skewed right, or normal. Therefore, option D is not true.
C) If the average is 70%, then half received grades above that score and half received grades below that score. So, option C is TRUE!
What is the name of a number that can be written in the form a + bi where a and b are nonzero real
numbers? (1 point)
a pure imaginary number
an imaginary unit
a real number
a complex number
Answer:
Complex numbers
Step-by-step explanation:
Given
[tex]a + bi[/tex]
Required
Determine the type of number in that form
Numbers written in [tex]a + bi[/tex] are referred to as complex numbers
Where [tex]a \neq 0[/tex]; [tex]b\neq 0[/tex] and [tex]i = \sqrt{-1}[/tex]
Note that a and b can either integers or non integers and a and be can also be positive or negative
The following are valid examples of complex numbers
[tex]2 + 3i[/tex]
[tex]2.4 - 5i[/tex]
[tex]-3 - i[/tex]
and lots more..
The net of a triangular prism is shown below. What is the surface area of the prism? A. 128 cm^2 B. 152 cm^2 C. 176 cm^2 D. 304 cm^2
Answer:
B. 152 cm²
Step-by-step explanation:
To find the surface area using a net, do this:
Take apart the figure. We see that there are three rectangles and two triangles. Find the area of each ([tex]A=l*w[/tex]) and then add the values together:
The first rectangle on the left is the same as the one on the right.
[tex]5*8=40[/tex]
Two measures are 40 cm².
The middle rectangle is:
[tex]6*8=48[/tex]
48 cm²
The formula for the area of a triangle is [tex]A=\frac{1}{2}*b*h[/tex]:
[tex]A=\frac{1}{2}*6*4\\\\A=\frac{1*6*4}{2}\\\\A=\frac{24}{2}\\\\ A=12[/tex]
The area of the two triangles is 12 cm².
Now add the values:
[tex]40+40+48+12+12=152[/tex]
The area of the figure is 152 cm².
:Done
What is the period of the function shown in the graph?
At origin, the value of the function is [tex]0[/tex]
and then it again becomes zero for the first time is at $2$
but the function isn't repeating itself (it's going downwards)
at $x=4$, it's exactly same, hence the period is $4$
2 less than five times a number.
Answer:
X will be the number.
5 times that number X is 5X
2 less than 5 times the number is 5X - 2
Hope this helps! Plz mark brainliest! （づ￣3￣）づ╭❤～
Answer
5x + 2
Step-by-step explanation:
5x + 2 or 5x - 2
I drive 13 miles each way to work every day. It sometimes takes me 20 minutes to get to work, and sometimes it takes me 30 minutes. If Distance = Rate x Time, at what rate am I going if it takes me 20 minutes to get to work? At 30 minutes?
Answer:
39 mph
26 mph
Step-by-step explanation:
distance = rate * time
20 minutes:
13 miles = rate * 20 minutes
rate = (13 miles)/(20 minutes) * (60 minutes)/(hour)
rate = 39 mph
30 minutes:
13 miles = rate * 30 minutes
rate = (13 miles)/(30 minutes) * (60 minutes)/(hour)
rate = 26 mph
Paula drives 130 miles in 2.5 hours. How far would she drive in 4.5 at the same speed?
*Please answer
I will award the Brainliest answer
Answer:
Paula will travel 234 miles in 4.5 hours
Step-by-step explanation:
Step 1: We first find the speed Paula is going in hours, we divide 130 mile by 2.5 hours to get 52 miles per hour
Step 2: We multiple 52 miles per hour with 4.5 hours to get 234 miles
Therefore Paula will travel 234 miles in 4.5 hours
Matrix A is said to be involutory if A2 = I. Prove that a square matrix A is both orthogonal and involutory if and only if A is symmetric.
Answer:
4 · 1/4 (I-0) = (A-0)∧2
see details in the graph
Step-by-step explanation:
Matrix A is expressed in the form A∧2=I
To proof that Matrix A is both orthogonal and involutory, if and only if A is symmetric is shown by re-expressing that
A∧2=I in the standard form
4 · 1/4 (I-0) = (A-0)∧2
Re-expressing
A∧2 = I as a graphical element plotted on the graph
X∧2=I
The orthogonality is shown in the graphical plot displayed in the picture. Orthogonality expresses the mutually independent form of two vectors expressed in their perpendicularity.
The numbers of words defined on randomly selected pages from a dictionary are shown below. Find the mean, median, mode of the listed numbers. 72 58 62 38 44 66 42 49 76 52 What is the mean? Select the correct choice below and ,if necessary ,fill in the answer box within your choice.(around to one decimal place as needed)
Answer:
72 58 62 38 44 66 42 49 76 52 ( arrange it!)
38 42 44 49 52 58 62 66 72 76 (done!)
Median: Find the number in the middle after we arranged, so the answer is (52+58)/2= 110/2 = 55
Mode : None (there is no number appear more than other number)
Mean = (38+42+44+49+52+58+62+66+72+76)/10
=559/100
=5,5
Hope it helps ^°^
will mark brainliest. PROMISE!! A stick has a length of $5$ units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are longer than $1$ unit?
Answer:
0.16
Step-by-step explanation:
Length = 5 unitsNumber of broken sticks= 3Equal lengths = 5 units/3See the picture attached for reference.
As you see the best points are the green areas which covers 2 out of 5 zones.
Since it is same for both broken points, the probability of this is:
2/5*2/5 = 4/ 25 = 0.16Answer is 0.16
Put these numbers in order from greatest to least.
8
-2-
25
2.45
-0.84
Answer:
25, 2.45, 8, -0.84, -2
Step-by-step explanation:
negative is a least number
positive is a greater number
Positive number-8, 25, 2.45
Negative number-(-2), -0.84
ordering number from greatest to least:
25, 2.45, 8, -0.84, -2
-2 is smallest then -0.84 because 2 is bigger then 0.84. It is opposite with the positive number.
The bigger the positive number the biggest it is. While the bigger the negative number the smallest it is.
Answer:
Step-by-step explanation:
The numbers are:
● 8
● -2
● 25
● 2.45
● -0.84
To make it easy classify the positive numbers apart and the negatives ones alone
● 2.45<8< 25
● -2 < -0.84
25 is the greatest and -2 is the least
● 25 > 8 > 2.45 > -0.84 > -2
find m<SPT in degrees
Answer: 60°
Step-by-step explanation:
∠UQR = 180°
∠UQR = ∠UQ + ∠QR
180° = 115° + ∠QR
65° = ∠QR
∠QRT = 180°
∠QRT = ∠QR + ∠RS + ∠ST
180° = 65° + ∠RS + 55°
180° = 120° + ∠RS
60° = ∠RS
Allowance bank received a deposit of 28,000 and is free to lend out 25,480 what is the reserve rate?
Answer:
Reserve rate = 9%
Step-by-step explanation:
Reserve ratio/rate is the percentage of deposits which commercial banks are required to keep as cash, as directed by the central banks.
first, let us calculate the reserve amount as follows:
Reserve = Deposit - (free amount to lend out)
Reserve = 28,000 - 25,480 = $2,520
[tex]Reserve\ rate = \frac{Reserves}{Deposits} \times100\\Reserve\ rate = \frac{2520}{28000} \times100\\=\frac{252000}{28000} =9\%[/tex]
Therefore the reserve rate = 9%
Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim (x, y) → (0, 0) x4 − 34y2 x2 + 17y2
Answer:
DNEStep-by-step explanation:
Given the limit of the function [tex]\lim_{(x,y) \to (0,0)} \frac{x^4-34y^2}{x^2+17y^2}[/tex], to find the limit, the following steps must be taken.
Step 1: Substitute the limit at x = 0 and y = 0 into the function
[tex]= \lim_{(x,y) \to (0,0)} \frac{x^4-34y^2}{x^2+17y^2}\\= \frac{0^4-34(0)^2}{0^2+17(0)^2}\\= \frac{0}{0} (indeterminate)[/tex]
Step 2: Substitute y = mx int o the function and simplify
[tex]= \lim_{(x,mx) \to (0,0)} \frac{x^4-34(mx)^2}{x^2+17(mx)^2}\\\\= \lim_{(x,mx) \to (0,0)} \frac{x^4-34m^2x^2}{x^2+17m^2x^2}\\\\\\= \lim_{(x,mx) \to (0,0)} \frac{x^2(x^2-34m^2)}{x^2(1+17m^2)}\\\\\\= \lim_{(x,mx) \to (0,0)} \frac{x^2-34m^2}{1+17m^2}\\[/tex]
[tex]= \frac{0^2-34m^2}{1+17m^2}\\\\= \frac{34m^2}{1+17m^2}\\\\[/tex]
Since there are still variable 'm' in the resulting function, this shows that the limit of the function does not exist, Hence, the function DNE
How do you find volume for prisms?
Answer:
V =140 units^3
Step-by-step explanation:
The volume of the prism is V = Bh
Where B is the area of the base and h is the height
B is the area of the triangle
B = 1/2 (5 * 7) = 35/2
V = 35/2 * 8
V =140 units^3
Of 900 people surveyed, 480 were male and 410 had cell phones. Of those with cell phones, 290 were female. What is the probability that a person surveyed was either male or had a cell phone? A. 600/900 = 0.6667 B. 770/900 = 0.8556 C. 360/900 = 0.40 D. 820/900 = 0.9111
Answer:
C. 360/900 = 0.40
Step-by-step explanation:
The number of the males that are using cellphone and the females who are using cell phones are in total 410. The total people surveyed are 900 people. There are total 480 males and rest 420 are females. Among the 420 females there are 290 females who use cellphones. The probability for males can be given by 360/900.
