Answer:
The 7th term is 10 and the 9th term is 16
(and the common difference d = 3)
Step-by-step explanation:
If by calculate the numbers, you mean the 7th term and 9th term, first, you will determine the common difference.
The nth term of an A.P is given by the formula
Tₙ= a+(n-1)d
Where Tₙ is the nth term
a is the first term
and d is the common difference
From the question,
a = -8
T₇ : T₉ = 5:8
From the formula
T₇ = a + (7-1)d = a + 6d
and T₉ = a + (9-1)d = a + 8d
Then.
a + 6d : a + 8d = 5:8
But a = -8
∴ -8 + 6d : -8 + 8d = 5:8
We can write that
(-8 + 6d) / (-8 + 8d) = 5/8
Cross multiply
8(-8+6d) = 5(-8+8d)
-64 + 48d = -40 + 40d
48d - 40d = -40 + 64
8d = 24
d = 24/8
d = 3
∴ The common difference is 3
Now, for the 7th term
From
T₇ = a + 6d
T₇ = -8 + 6(3)
T₇ = -8 + 18
T₇ = 10
and for the 9th term
T₉ = a + 8d
T₉ = -8 + 8(3)
T₉ = -8 + 24
T₉ = 16
Hence, the 7th term is 10 and the 9th term is 16
How is the graph of y=4(2)^x-3 translated from the graph of y=4(2)^x
Subtracting 3 at the end of the equation shifts the graph down 3 units
Power Function:
Analyze and model the power function: Exercise 1
(Correctly identify the function and later use it to answer the questions asked, including the development and the answer)
Answer:
The function is:
f(x) = axⁿAccording to data in the table we have:
f(1) = 3 ⇒ a(1)ⁿ = 3 ⇒ a*1 = 3 ⇒ a = 3f(2) = 12 ⇒ 3*2ⁿ = 12 ⇒ 2ⁿ = 4 ⇒ n = 2Since we found the values of a and n, the function becomes:
f(x) = 3x²The number of infected to the tenth day:
f(10) = 3*10² = 300can someone help me with this and show me how to do it?
9514 1404 393
Answer:
5i) f(x) = 3·13^x +5
5ii) f(x) = -6·(1/2)^x +5
6) f(x) = 3·8^x -1
9a) (1, 0), (0, -3)
9b) (2, 0), (0, 8)
Step-by-step explanation:
5. The horizontal asymptote is y = c. To meet the requirements of the problem, you must choose c=5 and any other (non-zero) numbers for 'a' and 'b'. (You probably want 'b' to be positive, so as to avoid complex numbers.)
i) f(x) = 3·13^x +5
ii) f(x) = -6·(1/2)^x +5
__
6. You already know c=-1, so put x=0 in the equation and solve for 'a'. As in problem 5, 'b' can be any positive value.
f(0) = 2 = a·b^0 -1
3 = a
One possible function is ...
f(x) = 3·8^x -1
__
9. The x-intercept is the value of x that makes y=0. We can solve for the general case:
0 = a·b^x +c
-c = a·b^x
-c/a = b^x
Taking logarithms, we have ...
log(-c/a) = x·log(b)
[tex]\displaystyle x=\frac{\log\left(-\dfrac{c}{a}\right)}{\log(b)}=\log_b\left(-\dfrac{c}{a}\right)[/tex]
Of course, the y-intercept is (a+c), since the b-factor is 1 when x=0.
a) x-intercept: log2(6/3) = log2(2) = 1, or point (1, 0)
y-intercept: 3-6 = -3, or point (0, -3)
b) x-intercept: log3(9/1) = log3(3^2) = 2, or point (2, 0)
y-intercept: -1 +9 = 8, or point (0, 8)
_____
Additional comment
It is nice to be comfortable with logarithms. It can be helpful to remember that a logarithm is an exponent. Even so, you can solve the x-intercepts of problem 9 using the expression we had just before taking logarithms.
a) 6/3 = 2^x ⇒ 2^1 = 2^x ⇒ x=1
b) -9/-1 = 3^x ⇒ 3^2 = 3^x ⇒ x=2
can anyone heelp me
b
Answer:
B. suggest that you and your boss schedule regular check-ins at lunchtime and at the end of the day
Step-by-step explanation:
It allows you to be ontask at your role (which you are hired for) while at the same time helps your boss know that you are on top of everything. It is the most polite option since you are setting professional boundaries but not complaining and showing frustrations.
(also so that your boss isn't micro-checking on you)
Hey guys not good at math please help
Answer:
3/2
Step-by-step explanation:
Recall that slope is y2 - y1 / x2 - x1.
Excellent. The question provides us with two points: (2,4) and (0,1). We can insert these two points into our equation.
Slope = (4 - 1) / (2 - 0) = 3 / 2.
Hope this helps!
Answer:
3/2
Step-by-step explanation:
(0,1) and (2,4)
(y2-y1)/(x2-x1)
= (4-1)/(2-0)
=3/2
Answered by GAUTHMATH
Translate sentence into inequality
A number c increased by 8 is greater than 30.
Step-by-step explanation:
the inequality is
[tex]c + 8 > 30[/tex]
find the derivative of e power ax divide by log bx
Answer:
Step-by-step explanation:
Ray’s weight increased by 11% in the last two years. If he gained 16.5 pounds, what was his weight two years ago?
Answer:
Ray weighed 150 pounds two years ago.
Step-by-step explanation:
11/100 = 16.5/x
11x = 16.5(100)
11x = 1,650
(11x)/11 = (1,650)/11
x = 150
About time that he should start going to the gym!
3a + 2b = 9
and
8x + y = 60
(i) What is the value of 9a + 6b?
(ii) What is the value of 4x + 3y?
Answer:
i dont kbow lol gggggggggg
Find the slope of the line containing the points (5, 3) and (-7, 2).
The sides of a triangle are in the ratio of 4:5:7 and its perimeter is 64. Find its sides
Answer:
16,20,28
Step-by-step explanation:
64 /(4+5+7)
64/16= 4
sides of triangle=4×4 :5×4: 7×4
=16:20:28
7+4i+1-3i simplify as much as possible
Answer:
8+i
Step-by-step explanation:
7+4i+1-3i
Combine like terms.
8+i
I hope this helps!
pls ❤ and give brainliest pls
solve the following ineuality -1+6(-1-3x) >-39-2x
Step-by-step explanation:
(=) 5 (-1-3x) >-39-2x
(=) -5-15x > -39-2x
(=) -13x > -34
=> x < 34/13
The pair of figures to the right are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number. Area of larger triangle = 165 ft^2 Thank you!!
9514 1404 393
Answer:
73 ft²
Step-by-step explanation:
The ratio of areas is the square of the ratio of linear dimensions.
smaller area = larger area × ((10 ft)/(15 ft))² = 165 ft² × (4/9)
smaller area = 73 1/3 ft² ≈ 73 ft²
Answer:
Area of the smaller triangle = 73 square feet
Step-by-step explanation:
Area of the larger triangle = 165 square feet
Area of a triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
[tex]\frac{1}{2}(\text{Base})(\text{Height})=165[/tex]
[tex]\frac{1}{2}(15)(\text{Height})=165[/tex]
Height = 22 ft
Since, both the triangles are similar.
By the property of similar triangles,
Corresponding sides of the similar triangles are proportional.
Let the height of smaller triangle = h ft
Therefore, [tex]\frac{h}{22}=\frac{10}{15}[/tex]
h = [tex]\frac{22\times 10}{15}[/tex]
h = 14.67 ft
Area of the smaller triangle = [tex]\frac{1}{2}(10)(14.67)[/tex]
= 73.33
≈ 73 square feet
-1/5y+7=7
What is the value of y?
An employee makes $11.20 per hour but is getting a 6.5% increase. What is his new wage per hour to the nearest cent? His new wage per hour is?
Answer:
11.93
Step-by-step explanation:
First find the amount of increase
11.20 *6.5%
11.20 *.065
0.728
Rounding to the nearest cent
.73
Add this to the original wage
11.20+.73
11.93
Compare –3.5 and . Use <, >, or =.
–3.5 >
–3.5 <
–3.5 =
Answer:
-3.5 > -4.5-3.5 < -1.5-3.5 = -3.5Step-by-step explanation:
Give any integer that suits the expression:-3.5 > -4.5-3.5 < -1.5-3.5 = -3.5• The farther a negative integer from 0, the smaller its value.[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Determine the coordinates of the ordered pairs on the coordinate grid.
Answer:
A = (5,7)
B = (0, -1)
C = (-8, -3)
D = (5, -8)
Step-by-step explanation:
Answer:
A = (5, 7)
B = (0, -1)
C = (-8, -3)
D = (5, -8)
To do these problems, trace along in a straight line from the coordinate to the x- axis line and then to the y-axis line. Whatever number you reach will be part of the coordinate.
Hope this helped.
On a recent trip to the convenience Store you picked up 4 gallons of milk 4 bottles of water and 5 snack size bags of chips your total was $28.35 if a bottle of water cost twice as much as a bag of chips and a gallon of milk cost $2.10 more than a bottle of water how much does each item cost
Answer:
The milk cost $2.10 each the snacks cost $1.535 each the water cost $3.07 each
Step-by-step explanation:
I think Im right
Of the travelers arriving at a small airport, 60% fly on major airlines, 20% fly on privately owned planes, and the remainder fly on commercially owned planes not belonging to a major airline. Of those traveling on major airlines, 50% are traveling for business reasons, whereas 70% of those arriving on private planes and 80% of those arriving on other commercially owned planes are traveling for business reasons. Suppose that we randomly select one person arriving at this airport.
What is the probability that the person
a. is traveling on business?
b. is traveling for business on a privately owned plane?
c. arrived on a privately owned plane, given that the person is traveling for business reasons?
d. is traveling on business, given that the person is flying on a commercially owned plane?
Answer:
a) 0.55 = 55% probability that the person is traveling on business
b) 0.14 = 14% probability that the person is traveling for business on a privately owned plane.
c) 0.2545 = 25.45% probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons.
d) 0.2 = 20% probability that the person is traveling on business, given that the person is flying on a commercially owned plane.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Question a:
50% of 60%(major airlines)
70% of 20%(privately owned airplanes)
80% of 100 - (60+20) = 20%(comercially owned airplanes). So
[tex]p = 0.5*0.5 + 0.7*0.2 + 0.8*0.2 = 0.55[/tex]
0.55 = 55% probability that the person is traveling on business.
Question b:
70% of 20%, so:
[tex]p = 0.7*0.2 = 0.14[/tex]
0.14 = 14% probability that the person is traveling for business on a privately owned plane.
Question c:
Event A: Traveling for business reasons.
Event B: Privately owned plane.
0.55 = 55% probability that the person is traveling on business.
This means that [tex]P(A) = 0.55[/tex]
0.14 = 14% probability that the person is traveling for business on a privately owned plane.
This means that [tex]P(A \cap B) = 0.14[/tex]
Desired probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.14}{0.55} = 0.2545[/tex]
0.2545 = 25.45% probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons.
Question d:
Event A: Commercially owned plane.
Event B: Business
80% of those arriving on other commercially owned planes are traveling for business reasons.
This means that:
[tex]P(B|A) = 0.2[/tex]
0.2 = 20% probability that the person is traveling on business, given that the person is flying on a commercially owned plane.
HELP PLEASE! I tried everything from adding to dividing, subtracting, multiplying but still no correct answer. Can someone help me out here please?
Answer:
46%
Step-by-step explanation:
Divde the smaller # by the bigger # to get the precentage
An average San Francisco customer uses what percent of electricity used by an average Houston customer?
In other words, San Francisco is what part of Houston?
---Just like, 7 is what part of 49? These are the same questions and would be solved in the same way
San Francisco / Houston
6753 / 14542
0.4644 = 46.44%
ANSWER: 46%
Hope this helps!
A random sample of n1 = 49 measurements from a population with population standard deviation σ1 = 3 had a sample mean of x1 = 9. An independent random sample of n2 = 64 measurements from a second population with population standard deviation σ2 = 4 had a sample mean of x2 = 11. Test the claim that the population means are different. Use level of significance 0.01.
Compute the corresponding sample distribution value. (Test the difference μ1 − μ2. Round your answer to two decimal places.)
Answer:
The answer is "-3.04"
Step-by-step explanation:
[tex]\to \bar{x_1}-\bar{x_2}=9-11=-2[/tex]
Sample distribution:
[tex]z=\frac{\bar{x_1}-\bar{x_2}- \bar{\mu_1}-\bar{\mu_2}}{\sqrt{\frac{\sigma_{1}^2}{n_1}+\frac{\sigma_{2}^2}{n_2}}}\\\\[/tex]
[tex]=\frac{(-2)-0}{\sqrt{\frac{3^2}{49}+\frac{4^2}{64}}}\\\\=\frac{-2}{\sqrt{\frac{9}{49}+\frac{16}{64}}}\\\\=\frac{-2}{\sqrt{\frac{576+784}{3136}}}\\\\=\frac{-2}{\sqrt{\frac{1360}{3136}}}\\\\=\frac{-2}{\sqrt{0.433}}\\\\=\frac{-2}{0.658}\\\\=-3.039\\\\=-3.04[/tex]
Solve d – 0.31 ≥ 1.87 Question 1 options: A) d ≤ 2.18 B) d = 2.18 C) d ≥ 1.56 D) d ≥ 2.18
Answer:
D) d ≥ 2.18
Step-by-step explanation:
d – 0.31 ≥ 1.87
d >_ 1.87 + 0.31
d >_ 2.18
What fraction is equivalent to 0.46464646...
A)
46∕999
B)
46∕99
C)
23∕50
D)
46∕100
Answer:
Hello,
answer is B
Step-by-step explanation:
[tex]0.\overline{46}=\dfrac{46}{99}[/tex]
The answer is a fraction with numerator is the period (46) and the denominator is a number made with 9 as longer that there are digits in the periode (here 2 digits ==> 99)
4 trillion = 4x 10million missing exponent
Answer:
3
Step-by-step explanation:
im pretty sure
A random sample of bolts is taken from inventory, and their lengths are measured. The average length in the sample is 5.3 inches with a standard deviation of .2 inches. The sample size was 50. The point estimate for the mean length of all bolts in inventory is
Answer:
[tex]L_x=5.3 inches[/tex]
Step-by-step explanation:
Average length [tex]\=x =5.3 inches[/tex]
Standard deviation [tex]\sigma=0.2 inches[/tex]
Sample size [tex]n=50[/tex]
Generally The point estimate for the mean length of all bolts in inventory is
[tex]L_x= \=x[/tex]
[tex]L_x=5.3 inches[/tex]
Help pls and thank you
What is the distance between the following points?
y
+
+++ 3
1 2 3 4 5 6 7 8 9
.
-27
-3+
-4
-5+
-6
-7
-8
Answer:
[tex]6\sqrt{2}[/tex]
Step-by-step explanation:
Answer:
8.49 or 6√2
Step-by-step explanation:
Use the distance formula to calculate the distance between the two points. The distance formula is √(x1-x2)^2+(y1-y2)^2 plug in (2,-3) and (8,-9) to get the solution of √72 or 8.49
The correlation between a student’s shoe size and their score on a final exam is −0.79.What conclusions can be drawn based on the correlation coefficient? Select all that apply.
There is a relationship between a student’s shoe size and their final exam score.Big shoe sizes correlate to low exam scores.Large shoe sizes cause students to do poorly on the final exam.As the shoe size decreases, the final exam score increases.Small shoe sizes cause students to do well on the final exam.
(1,2,4) (A,B,D)
Answer:
The first one, the second, and fourth one are correct.
Select A,B, and D.
ED2021
Answer:
A, B, and C
Step-by-step explanation:
I got it right ;)
The angle θ between 5i-j+k & 2i-j+k is
Step-by-step explanation:
Let,
[tex] \sf \vec{a} = 5 \hat{i} - \hat{j} + \hat{k} \\ \therefore \: \sf \: | \vec{a}| = \sqrt{ {5}^{2} + {( - 1)}^{2} + {1}^{2} } \\ = \sqrt{25 + 1 + 1} \\ = \sqrt{27} \\ \\ \sf \vec{b} = 2\hat{i} - \hat{j} + \hat{k} \\ \therefore \: \sf \: | \vec{b}| = \sqrt{ {2}^{2} + {( - 1)}^{2} + {1}^{2} } \\ = \sqrt{4 + 1 + 1} \\ = \sqrt{6} \\ \\\sf \: \vec{a}. \vec{b} = (5 \hat{i} - \hat{j} + \hat{k}).(2\hat{i} - \hat{j} + \hat{k}) \\ = 5 \times 2 + ( - 1) \times ( - 1) + 1 \times 1 \\ = 10 + 1 + 1 \\ = 12 \\ \\ \sf \: angle \: between \: \vec{a} \: and \: \vec{b} \: = \theta \\ \\ \: so \\ \sf \vec{a}. \vec{b} = | \vec{a}| . | \vec{b}| cos\theta \\ = > \sf \: cos \theta \: = \frac{ \vec{a}. \vec{b}}{ | \vec{a}| . | \vec{b}| } \\ = > cos \theta = \frac{12}{ \sqrt{27} \times \sqrt{6} } = 0.94 \\ = > \theta = {cos}^{ - 1} (0.94) \\ = > \green{\theta = 19.47 ^{ \circ} }[/tex]
