Answer:
The answer to this question can be defined as follows:
Step-by-step explanation:
In the question equation is missing so, the equation and its solution can be defined as follows:
[tex]B={b_1,b_2}\\\\b_1= \left[\begin{array}{c}5&5\end{array}\right] \ \ \ \ \b_2= \left[\begin{array}{c}2&-5\end{array}\right] \ \ \ \ \x= \left[\begin{array}{c}-7&-35\end{array}\right][/tex]
[tex]\left[\begin{array}{c}a&c\end{array}\right] =?[/tex]
[tex]\to \left[\begin{array}{c}-7&-35\end{array}\right]= a\left[\begin{array}{c}5&5\end{array}\right]+c \left[\begin{array}{c}2&-5\end{array}\right] \\[/tex]
[tex]\to \left[\begin{array}{c}-7&-35\end{array}\right]= \left[\begin{array}{c}5a+2c&5a-5c\end{array}\right]\\\\\to 5a+2c=-7....(1)\\\\\to 5a-5c=-35....(2)\\\\[/tex]
subtract equation 1 from equation 2:
[tex]\to 7c=28\\\\\to c=\frac{28}{7}\\\\\to c= 4\\\\[/tex]
put the value of c in equation 1
[tex]\to 5a+2(4)=-7\\\to 5a+8=-7\\\to 5a=-7-8\\\to 5a=-15\\\to a= -3[/tex]
coordinate value is [-3,4].
The price of a boat that Arthur wants is $29,450. Arthur finances this by paying $6000 down and monthly payment of $792.22 for 36 months.
a. Determine the amount to be financed.15a. _______________
b. Determine the installment price.b. _________________
c. Determine the finance charge.c. _________________
Answer:
see details below
Step-by-step explanation:
The price of a boat that Arthur wants is $29,450. Arthur finances this by paying $6000 down and monthly payment of $792.22 for 36 months.
a. Determine the amount to be financed.15a. ___$23450____________
29450 - 6000 = 23450
b. Determine the installment price.b. ___$792,22______________
"monthly payment of $792.22"
c. Determine the finance charge.c. __$5069.92_______________
A = 792.22
n = 36
finance charge = total paid - amount to be financed
= 36*792.22 - 23450
= 5069.92
What is the radius of a circle given by the equation x2 + y2 – 2x + 8y – 47= 0? radius = units
Answer:
8 units
Step-by-step explanation:
We need to rewrite an equation in the standard for a circle form.
r is radius.
(x−h)²+(y−k)²= r²
x² + y² – 2x + 8y – 47= 0
x² - 2x + y² + 8y - 47 = 0
x² - 2*x *1+ 1 ²- 1² + y² + 2*4*y + 4² - 4² - 47 = 0
(x - 1)² + (y + 4)² - 1 - 16 -47 =0
(x - 1)² + (y + 4)² - 64=0
(x - 1)² + (y + 4)² = 8²
Radius is 8.
The radius of the circle is 8 units
What is radius?The radius of a circle is a line drawn from the center to the circumference of the circle
The equation of the circle is given as;
[tex]x^2 + y^2 - 2x + 8y - 47 = 0[/tex]
Rewrite the equation as:
[tex]x^2 - 2x + y^2 + 8y = 47[/tex]
Next, we rewrite the equation in the standard form
So, we have:
x^2 - 2x + 1^2 - 1^2 + y^2 + 8y + 4^2 - 4^2 = 47
Evaluate the exponents
x^2 - 2x + 1 - 1 + y^2 + 8y + 16 - 16 = 47
Rewrite the equation as follows:
x^2 - 2x + 1 + y^2 + 8y + 16 = 47 + 1 + 16
Express as perfect squares
(x - 1)² + (y + 4)² = 64
(x - 1)² + (y + 4)² = 8^2
The radius of the circle is calculated as:
r^2 = 8^2
By comparison, we have:
r = 8
Hence, the radius of the circle is 8 units
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For the functions f(x)=4x−3 and g(x)=3x2+4x, find (f∘g)(x) and (g∘f)(x).
Answer:
(16x + 21) and (16x - 6)
Step-by-step explanation:
f(g(x)) = f(6 + 4x)
Applying the f(x) function on (6 + 4x) gives
4(6 + 4x) - 3
Which equals 16x + 24 - 3
= 16x + 21
g(f(x)) = g(4x - 3)
Applying the g(x) function on (4x - 3) gives
6 + 4(4x - 3)
Which equals 6 + 16x - 12
= 16x - 6
Answer:
(g∘f)(x)=48x2+48x+10
(g∘f)(x)=12x^2-6
Step-by-step explanation:
To find (f∘g)(x), use the definition of (f∘g)(x),
(f∘g)(x)=f(g(x))
Substituting 3x2−2 for g(x) gives
(f∘g)(x)=f(3x2−2)
Find f(3x2−2), where f(x)=4x+2, and simplify to get
(f∘g)(x)(f∘g)(x)(f∘g)(x)=4(3x2−2)+2=12x2−8+2=12x2−6
To find (g∘f)(x), use the definition of (g∘f)(x),
(g∘f)(x)=g(f(x))
Substituting 4x+2 for f(x) gives
(g∘f)(x)=g(4x+2)
Find g(4x+2), where g(x)=3x2−2, and simplify to get
(g∘f)(x)=3(4x+2)^2−2
(g∘f)(x)=48x2+48x+12−2
(g∘f)(x)=48x2+48x+10
M angle D=? What is the degree of the angle?
Answer:
80°Step-by-step explanation:
In ACB and ECD
AC =~ CE [ Given ]
BC =~ CD [ Given ]
<ACD =~ <ECD [ Vertical angles ]
Hence, ∆ ACB =~ ECD by SAS congruency of triangles.
Then, <B = <D
In ∆ABC , sum of all three angles must be 180°
<A + <B + <C = 180°
plug the values
[tex] 30 + < d \: + 70 = 180[/tex]
Add the numbers
[tex]100 + < d = 180[/tex]
Move constant to R.H.S and change it's sign
[tex] < d = 180 - 110[/tex]
Subtract the numbers
[tex] < d = 80[/tex] °
Hope this helps..
Best regards!!
A= 63°
C = 7.75 inch
B = 47°
Oblique Triangle
4. Refer to the oblique triangle shown. What's the size of angle C?
O A. 60°
B. 125°
O C. 45°
O D. 70°
Answer:
Option D is correct.
Angle C = 70°
Step-by-step explanation:
The sum of angles in a triangle = 180°
So,
(Angle A) + (Angle B) + (Angle C) = 180°
(Angle A) = 67°
(Angle B) = 43°
(Angle C) = ?
67° + 43° + (Angle C) = 180°
Angle C = 180 - 67 - 43 = 70°
Angle C = 70°
Hope this Helps!!!
What is the quotient? StartFraction 7 Superscript negative 4 Over 7 Superscript negative 9 EndFraction
Answer:
19
Step-by-step explanation:
7 supersricpt 8
What will happen to the median height of the outlier is removed?
{75, 63, 58, 59, 63, 62, 56, 59)
Answer:
The meadian decreases by 1.5 when the outlier is removed.
Step-by-step explanation:
Well first we need to find the median of the following data set,
(75, 63, 58, 59, 63, 62, 56, 59)
So we order the set from least to greatest,
56, 58, 59, 59, 62, 63, 63, 75
Then we cross all the side numbers,
Which gets us 59 and 62.
59 + 62 = 121.
121 / 2 = 60.5
So 65 is the median before the outlier is removed.
Now when we remove the outlier which is 75.
Then we order it again,
56, 58, 59, 59, 62, 63, 63
Which gets us 59 as the median.
Thus,
the median height decreases by 1.5 units when the outlier is removed.
Hope this helps :)
by what number 7whole 2/3be divided to get 4whole1/3
Answer: 1 30/39
Step-by-step explanation:
Because y/x=z and y/z=x are true with the same values, simply do 7 2/3 divided by 4 1/3 to get 69/39.
Hope it helps <3
select the fraction equivalent of 0.06. reduce to the lowest terms
Answer: 3/50
Step-by-step explanation:
0.06 = 6/100 , 100 would be the denominator because we have two figures after the decimal point. Each figures can also be represented by 10,
Again,
0.06 = 6 × 10-²
Now 0.06 = 6/100
= 3/50.
Therefore, the fractional form = 3/50 in its lowest term.
If there are 736 students in a school, prove that at least three students have a birthday on the same day of the year.
Step-by-step explanation:
736 / 365 = 2R6
So even if the first 365 students all have different birthdays, and the next 365 students also all have different birthdays, then there are 2 students for every birthday. The last 6 students therefore share a birthday with at least 2 other students. So there are at least 3 students who share a birthday.
Yes, we can prove that at least three students have a birthday on the same day of the year.
What is algebra?
Algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas.
We have,
Total number of students = 736
So,
In a year there are 365 days.
And we have 736 students,
So,
Two students have birthday on same day = 365 × 2 = 730
NOw,
Students left = 736 - 730 = 6
So,
These 6 Students share birthday with othe 6 Students .
So, yes there are at least three students who have a birthday on the same day of the year
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7.
The area of this parallelogram is 120 ft. Find the value of h.
1
20 ft
12 ft
3 ft
15 ft
6 ft
Answer:
h = 6 ft.Step-by-step explanation:
area = base x height
where base = 20 ft.
height = ?
area = 120 ft²
plugin values into the formula
120 = 20 x height
height = 120
20
height = 6 ft.
A simple random sample of 20 third-grade children from a certain school district is selected, and each is given a test to measure his/her reading ability. You are interested in calculating a 95% confidence interval for the population mean score. In the sample, the mean score is 64 points, and the standard deviation is 12 points. What is the margin of error associated with the confidence interval
Answer:
Margin of Error = ME =± 5.2592
Step-by-step explanation:
In the given question n= 20 < 30
Then according to the central limit theorem z test will be applied in which the standard error will be σ/√n.
Sample Mean = μ = 64
Standard Deviation= S= σ = 12
Confidence Interval = 95 %
α= 0.05
Critical Value for two tailed test for ∝= 0.05 = ±1.96
Margin of Error = ME = Standard Error *Critical Value
ME = 12/√20( ±1.96)=
ME = 2.6833*( ±1.96)= ± 5.2592
The standard error for this test is σ/√n
=12/√20
=2.6833
Need answers ASAP!!!!! (due today)
Answer:
15) 2.08m
Step-by-step explanation:
We kow tanA= p/b
Here, A=33°
b=3.2m
Then,
tan33°=p/3.2
0.65=p/3.2
p=0.65*3.2
p=2.08
So, The height of tree is 2.08m
14) 59.58ft
tan50°=p/b
1.19=p/50
p=59.58ft
So, The height of signpost is 59.58ft
In both of these problems, we will be using trigonometry! Remember, SOH-CAH-TOA.
14. x = 13.5950 ft
Visualization of the problem is attached below.
We want to find out the opposite side to the angle, and we know the adjacent side. Therefore, we should use the tangent function.
tan(50) = x / 50
x = tan(50) * 50
x = 13.5950 ft (round off wherever you need)
15. x = 241.0016 m
The visualization of the problem is already given. We know the same information as we need in the previous problems, an angle and an adjacent side, and we want to find the opposite side. Therefore, we should use the tangent function.
tan(33) = x / 3.2
x = tan(33) * 3.2
x = 241.0016 (round off wherever you need)
Hope this helps!! :)
1/6•4•(-1/3)•9•(-1/2)•5
Answer:
Step-by-step explanation:
its 5
1/6 *2 *3 *5=
1/3*3*5=
5
Over the last three evenings, Melissa received a total of 126 phone calls at the call center. The first evening, she received 6 more calls than the third evening. The second evening, she received 4 times as many calls as the third evening. How many phone calls did she receive each evening? Number of phone calls the first evening: Number of phone calls the second evening: Number of phone calls the third evening:
Answer:
calls first evening = 26
calls second evening = 80
calls third evening = 20
Step-by-step explanation:
Let x = calls third evening
x+6 = calls first evening
4x = calls second evening
x+6 + 4x + x = total calls = 126
Combine like terms
6x+6 = 126
Subtract 6 from each side
6x =120
Divide by 6
6x/6 =120/6
x = 20
x+6 = calls first evening = 20+6 = 26
4x = calls second evening = 4*20 = 80
Let x = calls third evening = 20
What rule (i.e. R1, R2, R3, R4, or R5) would you use for the hawk and for the grizzly bear? a. R2 and R5 b. R1 and R3 c. None of the above d. R1 and R4
Answer:
I NEED POINTS
Step-by-step explanation:
A Canadian longitudinal study1 examined whether giving antibiotics in infancy increases the likelihood that the child will be overweight later in life. The study included children and found that of the children had received antibiotics during the first year of life. Test to see if this provides evidence that more than of Canadian children receive antibiotics during the first year of life. Show all details of the hypothesis test, including hypotheses, the standardized test statistic, the -value, the generic conclusion using a significance level, and a conclusion in context.
1. Clearly state the null and alternative hypotheses.
2. Calculate the test statistic and p-value.
3. What is the conclusion?
4. Do we have evidence to conclude that more than 70% of Canadian infants receive antibiotics?
A. Yes
B. No
Answer:
1. [tex]H_{0}[/tex] : p = 0.70 , [tex]H_{a}[/tex] : p > 0.70
2. Test Statistic : 0.54 , P value : 0.2946
3. Fail to reject null Hypothesis
4. No.
Step-by-step explanation:
1. Null hypothesis is 70% of children receive antibiotics.
Alternative hypothesis is more than 70% of children receive antibiotics.
2. Test statistic is calculated as;
z = [tex]\frac{p (1 - p)}{\sqrt{\frac{p (1-p}{n} )} }[/tex]
z = [tex]\frac{0.01}{0.0185}[/tex]
z = 0.54
3. p value is calculated as;
1 - right tailed probability
1 - 0.7054 = 0.2946
.If you add 5 to both the numerator and the denominator of a fraction, you obtain 2/3; however, if '
you subtract 5 from both the numerator and the denominator of the same fraction, you obtain 1/4. For what fraction is this true?
Answer:
The fraction that this is true for = 7/13
Step-by-step explanation:
From the above question
Let the numerator be represented by a
Let the denominator be represented by b
If you add 5 to both the numerator and the denominator of a fraction, you obtain 2/3
This means:
a + 5/b + 5 = 2/3
Cross Multiply
3(a + 5) = 2(b + 5)
3a + 15 = 2b + 10
Collect like terms
3a - 2b = 10 - 15
3a - 2b = -5..........Equation 1
If you subtract 5 from both the numerator and the denominator of the same fraction, you obtain 1/4
This means:
a - 5/b - 5 = 1/4
Cross Multiply
4(a - 5) = 1(b - 5)
4a - 20 = b - 5
Collect like terms
4a - b = 20 - 5
4a - b = 15..........Equation 2
b = 4a - 15
3a - 2b = -5..........Equation 1
4a - b = 15..........Equation 2
Substitute 4a - 15 for b in equation 1
3a - 2b = -5..........Equation 1
3a - 2(4a - 15) = -5
3a - 8a + 30 = -5
Collect like terms
3a - 8a = -5 - 30
-5a = -35
a = -35/-5
a = 7
Therefore, the numerator of the fraction = 7
Substitute 7 for a in Equation 2
4a - b = 15..........Equation 2
4 × 7 - b = 15
28 - b =15
28 - 15 = b
b = 13
The denominator = b is 13.
Therefore,the fraction which this is true for = 7/13
To confirm
a) If you add 5 to both the numerator and the denominator of a fraction, you obtain 2/3
This means:
a + 5/b + 5 = 2/3
7 + 5/ 13 + 5 = 2/3
12/18 = 2/3
Divide numerator and denominator by of the left hand side by 6
12÷ 6/ 18 ÷ 6 = 2/3
2/3 =2/3
If you subtract 5 from both the numerator and the denominator of the same fraction, you obtain 1/4
This means:
a - 5/b - 5 = 1/4
7 - 5/13 - 5 = 1/4
2/8 = 1/4
Divide the numerator and denominator of the left hand side by 2
2÷2/8 ÷ 2 = 1/4
1/4 = 1/4
From the above confirmation, the fraction that this is true for is 7/13
Below are the jersey numbers of 11 players randomly selected from a football team. Find the range, variance, and standard deviation for the given sample data.
33 29 97 56 26 78 83 74 65 47 58
What do the results tell us?
A. Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.
B. Jersey numbers on a football team vary much more than expected.
C. The sample standard deviation is too large in comparison to the range.
D. Jersey numbers on a football team do not vary as much as expected.
Answer:
Option(A) is correct
Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.
Step-by-step explanation:
The given data set in the question are ;33, 29, 97, 56, 26, 78, 83, 74, 65, 47, 58
the range can be determined by finding the highest value and subtract it to the lowest value. In this case the values are:
Highest = 97
Lowest = 71
Range = highest value - Minimum value
Range = 97 - 26 = 71
[tex] Range= 71[/tex]
mean of the data is the summation of all the numbers in the data set divided by the number of given samples.
Mean = (33 + 29 + 97 + 56+ 26 + 78 + 83 74+ 65 + 47 + 58)/11
= 647/11
[tex]Mean value =58.7[/tex]
Now to find the variance of the data set by using below formular
σ²=[ (xᵢ -mean)²]/n-1
[(33-58.7)² +(29-58.7)²+( 97-58.7)²+( 56-58.7)²+( 26 -58.7)²+(78-58.7)²+( 83 -58.7)²+(74-58.7)²+( 65-58.7)²+( 47 -58.7)²+(58 -58.7)²]/10
[tex]Variance=546[/tex]
Now, we will calculate standard deviation by taking square root over variance
σ =√(variance)
σ =√(546)
[tex]Standard deviation= 23.4[/tex]
Hence, the range is 71 ,variance is 546 and standard deviation is 23.4 therefore,
Option A is the answer that is Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.
In a random sample of 400 residents of Boston, 320 residents indicated that they voted for Obama in the last presidential election. Develop a 95% confidence interval estimate for the proportion of all Boston residents who voted for Obama.
Answer:
C.I = 0.7608 ≤ p ≤ 0.8392
Step-by-step explanation:
Given that:
Let consider a random sample n = 400 candidates where 320 residents indicated that they voted for Obama
probability [tex]\hat p = \dfrac{320}{400}[/tex]
= 0.8
Level of significance ∝ = 100 -95%
= 5%
= 0.05
The objective is to develop a 95% confidence interval estimate for the proportion of all Boston residents who voted for Obama.
The confidence internal can be computed as:
[tex]=\hat p \pm Z_{\alpha/2} \sqrt{\dfrac{ p(1-p)}{n } }[/tex]
where;
[tex]Z_{0.05/2}[/tex] = [tex]Z_{0.025}[/tex] = 1.960
SO;
[tex]=0.8 \pm 1.960 \sqrt{\dfrac{ 0.8(1-0.8)}{400 } }[/tex]
[tex]=0.8 \pm 1.960 \sqrt{\dfrac{ 0.8(0.2)}{400 } }[/tex]
[tex]=0.8 \pm 1.960 \sqrt{\dfrac{ 0.16}{400 } }[/tex]
[tex]=0.8 \pm 1.960 \sqrt{4 \times 10^{-4}}[/tex]
[tex]=0.8 \pm 1.960 \times 0.02}[/tex]
[tex]=0.8 \pm 0.0392[/tex]
= 0.8 - 0.0392 OR 0.8 + 0.0392
= 0.7608 OR 0.8392
Thus; C.I = 0.7608 ≤ p ≤ 0.8392
Question 8(Multiple Choice Worth 1 points) (07.01 MC) Find the measure of arc DF. Circle A with chords EF and CD that intersect at point G, the measure of arc EC is 5x plus 10 degrees, the measure of angle EGC is 70 degrees, and the measure of arc DF is 11x plus 2 degrees. 50° 90° 100° 140°
Answer: 90°
Step-by-step explanation:
As known ∡EGC=(arcEC+arcDF)/2
arcEC+arcDF=70°*2
5x+10+11x+2=140
16x+12=140
16x=128
x=128:16
x=8
So arcDF=11*x+2=11*8+2=90°
The measure of arc DF is 90°.
What is circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.
Given, Circle A with chords EF and CD that intersect at point G,
arc EC = 5x + 10°
arc DF = 11x + 2°
∠EGC = 70°
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite
so
∠EGC=(1/2)[arc EC+arc DF]
substitute the values
70 = 1/2(5x + 10 + 11x + 2)
70 = 1/2(16x + 12)
140 = 16x + 12
16x = 128
x = 128/16 = 8
so ac DF = 11x + 2
arc DF = 11(8) + 2
arc DF= 88 + 2 = 90°
Hence the value of arc DF is 90°.
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Whal value of x is in the solution set of 9(2x + 1) < 9x - 18?
A: -4
B: -3
C: -2
D: -1
Answer:
A:-4
Step-by-step explanation:
If you simplify 9(2x+1)<9x-18 you will get 9x<-27. That will mean x<-3 and the only answer for something less than -3 is -4.
If the answer was right, please put 5 stars.
Answer:
The answer would be-4
Step-by-step explanation:
Here,
9(2x+1) < 9x-18
or, 18x+9 < 9x-18
or, 18x-9x<-18-9
or, 9x<-27
or, x= -27/9
Therefore, the value of x is -4.
Hope it helps...
Which graph best models the inequality y<_ -2/5x+2
Answer:
Step-by-step explanation:
Simplify each term.
y ≤ −2x/5 + 2
Find the slope and the y-intercept for the boundary line.
Slope: -2/5
Y-intercept: 2
Graph a solid line, then shade the area below the boundary line since
y is less than -2x/5 + 2
y ≤ −2x/5 + 2
Hope this can help
What is the inequality
Answer:
x ≥ 4
Step-by-step explanation:
Well to find the inequality we need to single out x,
4x - 1 ≥ 15
+1 to both sides
4x ≥ 16
Divide 4 by both sides
x ≥ 4
Thus,
x is greater than or equal to 4.
Hope this helps :)
determining the probability of events. please help :)
Answer:
C. 1/8
Step-by-step explanation:
Probability of shooting a goal on a throw is 2/4 = 1/2.
Probability of 3 in a row is (1/2)³ = 1/8.
Find the value of n such that 540n is perfect cube.
Answer:
1.35
Step-by-step explanation:
next cube above 540 is 729
to get to 729: 729 / 540 = 1.35
n = 1.35
What are the dimensions of the rectangle? PLEASE HELP!!
Answer:
2(x^2 + 8x -55)
Step-by-step explanation:
Well to do the box method we first need to simplify the given equation further to,
[tex]2x^2 + 16x - 110\\[/tex],
For this quadratic the box method doesn't work so we can divide everything by 2 make make it
2(x^2 + 8x -55)
Thus,
[tex]2x^2 + 16x - 110\\[/tex] factored is 2(x^2 + 8x -55).
Hope this helps :)
Lines $y=(3a+2)x-2$ and $2y=(a-4)x+2$ are parallel. What is the value of $a$?
Answer:
-8/5Step-by-step explanation:
Given two lines y=(3a+2)x-2 and 2y=(a-4)x+2, Since both lines are parallel to each other, this means that the slope of both lines are the same
Let's get the slope of both equation. For the first equation;
y=(3a+2)x-2
We can see that the equation is written in this form y = mx+c where m is the slope of the line. On comparison, the slope of the given line is 3a+2
Similarly for the second line;
2y=(a-4)x+2
Re-writing in the standard format we will have;
y = (a-4)x/2+2/2
y = (a-4)x/2 + 1
The slope of the second line is (a-4)/2
On equating the slope of both lines to get the value of 'a' we will have;
3a+2 = (a-4)/2
Cross multiplying
2(3a+2) = a-4
6a+4 = a-4
Collecting like terms;
6a-a = -4-4
5a = -8
a = -8/5
Hence the value of a is -8/5
A father is 60 years old and his son is half his age. How old was the boy when his father was four times his age?
Hey there! I'm happy to help!
We see that the father is 60 years old, and the son is half of that age, so this means that the son is 30 years old.
We want to see the age the son was at when the father was four times his age. We know that the father is thirty years older than him, so we can write this equation with s representing the age of the son.
s+30=4s (30 years older than the son is equal to to four times the son's age at the time)
We subtract 30 from both sides.
s=4s-30
We subtract 4s from both sides.
-3s=-30
We divide both sides by -3.
s=10
Therefore, the boy was 10 when his father was four times his age. This is because his father would have been 40 because that is 30 more years than 10, and it is four times ten!
Have a wonderful day! :D
Which equation represents a population of 250 animals that decreases at an annual rate of 21%
Answer:
y= 250( 1-0.21)^x
Step-by-step explanation:
This represents exponential decay
The equation represents a population of 250 animals that decreases at an annual rate of 21% will be p = 250(0.79)[tex].^t[/tex] The correct option is C.
What is an exponential function?The mathematical expression f(x)=[tex]e^t[/tex] denotes the exponential function. The term typically refers to the positive-valued function of a real variable, unless otherwise specified.
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
It is given that a population of 250 animals is decreasing at an annual rate of 21%.
p = a x b[tex].^t[/tex]
p = a x (1+r)[tex].^t[/tex]
p = 250 x (1+(-0.21))[tex].^t[/tex]
p = 250(0.79)[tex].^t[/tex]
Note that r = -0.21 is negative to indicate we have exponential decay.
Hence, the equation represents a population of 250 animals that decreases at an annual rate of 21% will be p = 250(0.79)[tex].^t[/tex] The correct option is C.
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