a. The interest that would accrue at Bank A is $1484.32.
b. Kathy would owe $5984.32 at Bank A.
c. The interest that would accrue at Bank B is $201.82.
d. Kathy would owe $4776.82 at Bank B.
e. Kathy would save $1213.03 by using Bank B.
a. The annual interest at Bank A is 21.99%. The simple interest for 18 months can be calculated as:
I = Prt = 4500 x 0.2199 x (18/12) = $1484.32.
Therefore, the interest that would accrue at Bank A is $1484.32.
b. The total amount that Kathy would owe at Bank A is the sum of the principal and interest:
Total = Principal + Interest = $4500 + $1484.32. = $5984.32.
Therefore, Kathy would owe $5984.32 at Bank A.
c. The annual interest rate at Bank B is 2.99%, but there is also a one-time service fee of $75. The interest for 18 months can be calculated as:
I = Prt = 4500 x 0.0299 x (18/12) = $201.82.
Therefore, the interest that would accrue at Bank B is $201.82.
d. The total amount that Kathy would owe at Bank B is the sum of the principal, interest, and service fee:
Total = Principal + Interest + Service fee = $4500 + $201.82 + $75 = $4776.82
Therefore, Kathy would owe $4776.82 at Bank B.
e. By using Bank B, Kathy would save the difference between the total amount owed at Bank A and the total amount owed at Bank B:
Savings = Total at Bank A - Total at Bank B = $5989.85 - $4776.82 = $1213.03.
Therefore, Kathy would save $1213.03 by using Bank B.
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how would you show your work for this problem?
3x - 5 = x + 2 - 10 - 7x
Answer: x = [tex]-\frac{1}{3}[/tex]
Step-by-step explanation:
To show your work for this problem, you will write out every step that you take to solve for x.
Given:
3x - 5 = x + 2 - 10 - 7x
Combine like terms:
3x - 5 = - 6x - 8
Add 5 and 6x to both sides of the equation:
9x = - 3
Divide both sides of the equation by 9 and simplify the fraction:
x = [tex]-\frac{3}{9}=-\frac{1}{3}[/tex]
1. Find the sum of the first six terms of the geometric sequence for which a2 = 0.7 and a3 = 0.49.
A. Rewrite using radicals.
B. Rewrite using rational exponents.
a)
The sum of the first six terms of the given geometric sequence is approximately 0.92.
b)
The sum of the first six terms of the given geometric sequence is approximately 0.92.
We have,
A.
We know that for a geometric sequence, the ratio of consecutive terms is constant.
Let's call this ratio "r".
So, we have:
a2/a1 = r
a3/a2 = r
Substituting the given values, we get:
0.7/a1 = r
0.49/0.7 = r
Simplifying the second equation:
r = 0.7/0.49 = 1.4286...
Substituting this value in the first equation:
0.7/a1 = 1.4286...
Solving for a1:
a1 = 0.7/1.4286... = 0.49
Now we can use the formula for the sum of the first n terms of a geometric sequence:
Sn = a1(1 - r^n)/(1 - r)
Substituting the values we have found, and using n = 6, we get:
S6 = 0.49(1 - 1.4286^6)/(1 - 1.4286) ≈ 0.92
B.
We can rewrite the formula for the sum of the first n terms of a geometric sequence using rational exponents as:
Sn = a1(1 - r^n)/(1 - r^(1/n))
Substituting the values we have found, and using n = 6, we get:
S6 = 0.49(1 - 1.4286^6)/(1 - 1.4286^(1/6))^(6)
Simplifying the expression using a calculator, we get:
S6 ≈ 0.92
Therefore,
The sum of the first six terms of the given geometric sequence is approximately 0.92.
The sum of the first six terms of the given geometric sequence is approximately 0.92.
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For the second week of November, Donald Miller worked 52 hours. Donald earns $13 an hour. His employer pays overtime for all hours worked in excess of 40 hours per week and pays 1.5 times the hourly rate for overtime hours.
Calculate the following for the second week of November (round your responses to the nearest cent if necessary):
For the second week of November, Donald Miller earned $754.
Let's calculate Donald Miller's earnings for the second week of November using the given information:
1. Determine the number of regular and overtime hours:
Donald worked 52 hours in total, with overtime paid for hours above 40. So he worked 40 regular hours and 12 overtime hours (52 - 40 = 12).
2. Calculate regular pay:
Donald earns $13 per hour for the regular hours. To find his regular pay, multiply the hourly rate by the number of regular hours worked: 40 hours * $13/hour = $520.
3. Calculate overtime pay:
The overtime rate is 1.5 times the hourly rate, so the overtime pay is $13 * 1.5 = $19.5 per hour. To find the total overtime pay, multiply the overtime rate by the number of overtime hours worked: 12 hours * $19.5/hour = $234.
4. Calculate the total pay for the second week of November:
Add the regular pay and overtime pay together: $520 (regular pay) + $234 (overtime pay) = $754.
So, for the second week of November, Donald Miller earned $754 (rounded to the nearest cent if necessary).
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A nursing student can be assigned to one of five different floors each day depending on staffing needs. How many different ways can she be assigned during a -day work week?
There are 3125 different ways the nursing student can be assigned to different floors during a 5-day work week.
To determine the number of different ways a nursing student can be assigned to one of five different floors each day during a 5-day work week, we need to calculate the total number of possibilities.
Since the student can be assigned to any of the five floors each day, there are 5 options for each day. Since there are 5 days in a work week, we multiply the number of options for each day together:
Total number of possibilities = 5 options per day × 5 options per day × 5 options per day × 5 options per day × 5 options per day
Total number of possibilities = [tex]5^5[/tex] = 3125
Calculating this value, we find that there are 3125 different ways the nursing student can be assigned to different floors during a 5-day work week.
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The table lists the probabilities of Amy, Susan, Mark, Nina, and Jeff studying on a Sunday. It also gives the average number of hours each one of them studies.
Amy Susan Mark Nina Jeff
Probability 0.23 0.31 0.17 0.19 0.10
Average Hours of Studying 2.5 1.5 3 2 4.5
If you select 10 Sundays from the school year at random,
is likely to have studied the most hours overall, and
is likely to have studied the least hours overall.
Based on the given probability values, Mark is likely to have studied the most hours overall, and Amy is likely to have studied the least hours overall when selecting 10 Sundays from the school year at random.
What is the expected number of hours for each person?The expected number of hours for each person is determined by multiplying the probability of studying on a Sunday by the average number of hours of studying.
Amy: 0.23 * 2.5 = 0.575
Susan: 0.31 * 1.5 = 0.465
Mark: 0.17 * 3 = 0.51
Nina: 0.19 * 2 = 0.38
Jeff: 0.1 * 4.5 = 0.45
From the calculations, we can see that Mark is likely to have studied the most hours overall with an expected value of 0.51. Amy is likely to have studied the least hours overall with an expected value of 0.575.
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Scale practice for 7th grade geometry
Step-by-step explanation:
what is the question that you are asking?
100 Points! Graph the function. State the domain and range. Photo attached. Thank you!
The domain of the function is all real numbers (x ∈ R) and the range is all positive real numbers (y > 0).
The set of all values of the independent variable for which the function is defined is known as domain.
The function is defined for all real values of x so domain is R.
Domain: x ∈ R
The range of a function is the set of all values of the dependent variable (usually denoted as 'y') that the function can take as x varies over its domain.
For this function, the base of the exponent is 2, which means that the function grows exponentially as x increases.
As such, the range of this function is all positive real numbers.
Range: y > 0
Therefore, the domain of the function is all real numbers (x ∈ R) and the range is all positive real numbers (y > 0).
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Help please answer the number 2 only thanyou
i will give brainliest
Answer:
[tex]\sin\beta=\dfrac{8}{17}[/tex]
[tex]\cos\beta=\dfrac{15}{17}[/tex]
[tex]tan\beta=\dfrac{8}{15}[/tex]
[tex]\csc\beta=\dfrac{17}{8}[/tex]
[tex]\cot\beta=\dfrac{15}{8}[/tex]
Step-by-step explanation:
The secant ratio is the reciprocal of the cosine ratio.
[tex]\sec \beta= \dfrac{1}{\cos \beta}[/tex]
Therefore, if sec β = 17/15 then:
[tex]\dfrac{1}{\cos \beta}=\dfrac{17}{15}[/tex]
[tex]\cos \beta=\dfrac{15}{17}[/tex]
The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse of a right triangle:
[tex]\cos\beta= \sf \dfrac{adjacent}{hypotenuse}[/tex]
Therefore, the length of the side adjacent angle θ is 15 and the length of the hypotenuse is 17.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
We can use Pythagoras Theorem to calculate the length of the side opposite angle β:
[tex]15^2+O^2=17^2[/tex]
[tex]O^2=17^2-15^2[/tex]
[tex]O=\sqrt{17^2-15^2}[/tex]
[tex]O=\sqrt{64}[/tex]
[tex]O=8[/tex]
Therefore, the length of the side opposite angle β is 8.
Now we have the lengths of the three sides of the right triangle, we can find the other trigonometric function of angle β.
[tex]\boxed{\begin{minipage}{8cm}\underline{Trigonometric functions}\\\\$\sf \sin\beta=\dfrac{O}{H}\quad\cos\beta=\dfrac{A}{H}\quad\tan\beta=\dfrac{O}{A}$\\\\\\$\sf\csc\beta=\dfrac{H}{O}\quad\sec\beta=\dfrac{H}{A}\quad\cot\beta=\dfrac{A}{O}$\\\\\\where:\\\phantom{ww}$\bullet$ $\beta$ is the angle.\\\phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle.\\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse.\\\end{minipage}}[/tex]
Given values:
O = 8A = 15H = 17Substitute these values into the six trigonometric functions:
[tex]\sin\beta=\dfrac{O}{H}=\dfrac{8}{17}[/tex]
[tex]\cos\beta=\dfrac{A}{H}=\dfrac{15}{17}[/tex]
[tex]tan\beta=\dfrac{O}{A}=\dfrac{8}{15}[/tex]
[tex]\csc\beta=\dfrac{H}{O}=\dfrac{17}{8}[/tex]
[tex]\sec\beta=\dfrac{H}{A}=\dfrac{17}{15}[/tex]
[tex]\cot\beta=\dfrac{A}{O}=\dfrac{15}{8}[/tex]
x/1+5>5 solve the inequality
Answer:
x > 0
Step-by-step explanation:
To solve the inequality x/1 + 5 > 5, we first need to isolate the variable on one side of the inequality.
Subtracting 5 from both sides gives:
x/1 > 0
Multiplying both sides by 1 gives:
x > 0
Therefore, the solution to the inequality is x > 0.
Which descriptions represent a categorical data set?
Select all correct answers.
a.) average length of time that a piece of chewing gum is chewed
b.) color of chewing gum brands sold at Store A
c.) best selling chewing gum flavors
d.) number of packages of chewing gum sold in town in a day
e.) names of stores that carry Brand X of chewing gum
The descriptions that represent a categorical data set are: Color of chewing gum brands sold at Store A, Best selling chewing gum flavors, Names of stores that carry Brand X of chewing gum.
We know that,
A data set is a collection of data, usually presented in tabular form, that can be analyzed to draw conclusions or make decisions. It can be numerical or categorical and can come from various sources such as surveys, experiments, or observations.
A data set typically contains individual data points or observations, each representing a unit or subject being studied. The size of a data set can range from small (e.g., a few observations) to large (e.g., millions of observations).
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6. Trini is allowed to play video games no more than 4 hours over the weekend. Graph the
inequality on a number line.
this year. If a represents the number
The number of hours they can play video games before the weekend, then the inequality that represents the situation will be:
8 - a ≤ 4
Noted that inequality is a mathematical statement that compares two quantities or expressions that are not equal using the inequality signs such as:
Given that Trini is allowed to play video games no more than 4 hours over the weekend.
A number of hours to be played during the weekend is given as, at least 4 hours. This means the number of hours to play at the weekend can be 4 hours or more.
If a represents the number of hours they can play video games before the weekend, then the inequality that represents the situation will be:
8 - a ≤ 4
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How does the lasso penalty differ from the ridge penalty in shrinkage models, and
what effect does this difference have on the estimated coefficient?
The choice between the two depends on the specific problem and desired model characteristics. The lasso penalty may be preferred when the goal is to identify a small number of important predictors, while the ridge penalty may be preferred when the goal is to retain all predictors in the model but reduce their impact.
The lasso penalty and the ridge penalty are two different approaches to shrinkage models in which the goal is to reduce the complexity of a model by shrinking the coefficients towards zero. The main difference between the lasso penalty and the ridge penalty is in the way they perform this shrinking.
The lasso penalty uses an L1 norm, which encourages sparsity by driving some coefficients to exactly zero. This means that the lasso penalty is able to perform variable selection by completely eliminating some predictors from the model. In contrast, the ridge penalty uses an L2 norm, which does not drive coefficients to exactly zero, but rather shrinks them towards zero. This means that the ridge penalty is not able to perform variable selection in the same way as the lasso penalty.
The effect of this difference on the estimated coefficient is that the lasso penalty tends to produce more sparse models with fewer non-zero coefficients, while the ridge penalty tends to produce models with more non-zero coefficients. The lasso penalty may be preferred when the goal is to identify a small number of important predictors, while the ridge penalty may be preferred when the goal is to retain all predictors in the model but reduce their impact.
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3. Prepare a contribution margin income statement.
Naomi's Quilt Shoppe sells homemade Amish quilts. Naomi buys the quilts from local
Amish artisans for $290 each, and her shop sells them for $490 each. She also pays a
sales commission of 8% of sales revenue to her sales staff. Naomi leases her country-
style shop for $1,300 per month and pays $1,800 per month in payroll costs in addition
to the sales commissions. Naomi sold 95 quilts in February,
According to Naomi's Quilt Shoppe's contribution margin income statement, she had a net income of $12,176 for the month of February.
To solve this problemFor the month of February, Naomi's Quilt Shoppe's contribution margin income statement is as follows:
Revenue from Sales: 95 x $490 = 46,550
Cost of Goods Sold: 95 x $290 = $27,550
Gross profit: $27,550 - $46,550 = $19,000.
Variable expenses :
Revenue Commission: 8% × $46,550 = $3,724
Costs for all variables: $3,724
Contribution Margin: $19,000 - $3,724 = $15,276
Fixed expenses :
Rent: $1,300
Cost of payroll: $1,800
Total Fixed Costs: $3,100
Net Income: $15,276 - $3,100 = $12,176
Therefore, According to Naomi's Quilt Shoppe's contribution margin income statement, she had a net income of $12,176 for the month of February.
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For the right triangles below, find the values of the side lengths h and a.
Round your answers to the nearest tenth.
60°
(a) h=
h
(b) a=
a= 0
30°
5
X
45°
a
7
45%
(a) The value of h in the right triangle is 5.8.
(b) The value of a in the right triangle is 9.9.
What is a right triangle?Right triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle), i.e, in which two sides are perpendicular.
(a) To find the value of h in the right triangle, we use the formula below
Formula:
h = A/sin∅.................. Equation 1Where:
A = 5∅ = 60°Susbtituet these values into equation 1
h = 5/sin60°h = 5/0.8660h = 5.8(b) Also, to calculate the value of a in the right triangle, we us the formula below
a = B/sinθ................................. Equation 2Where:
B = 7θ = 45°Substitute these values into equation 2
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If a horse can jump a fence that is 4 feet tall, can you jump a fence that is 7/6 of a yard (please explain algebraically how to find this) (this is from unit 8 Algebra 1 if that helps)
Answer:
3.5 feet
Step-by-step explanation:
To determine whether you can jump a fence that is 7/6 of a yard tall, we need to convert the height to feet and compare it to your own jumping ability.
1 yard = 3 feet
So, 7/6 yards = (7/6) x 3 feet = 3.5 feet
Since a horse can jump a fence that is 4 feet tall and 4 feet is greater than 3.5 feet, it is likely that the horse can jump the fence while it may be more challenging for you to do so.
A bag contains 3 gold marbles, 7 silver marbles, and 20 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1.
What is your expected value if you play this game?
5
Functional Volume Questions ACCESS MATHS
1) James has a swimming pool in the shape of a prism.
Diagram NOT
18m
Accurately drawn
3m
6m
1m
топол хочите
9m
The swimming pool is empty.
It is filled with water at a constant rate.
It takes 4 hours for the water to be 2 meters deep from the deepest
point.
a) How long will it take to completely fill the pool?
Give your answer in hours.
(1m³ = 1000litres)
You must show all your working.
The amount of time it will take to completely fill the pool would be = 18 hours.
How to calculate the amount of time taken to fill the pool?To determine the amount of time it will take to fill the pool, the volume of the pool is first calculated by dividing the figure to obtain two regular shapes of a trapezoidal prism and a square prism.
The volume of a trapezoidal prism = 1/2(a+b)×h×l
where;
a = 3m
b = 1m
h = 18-6 = 12m
l = 9m
Volume of the trapezoidal prism = 1/2(3+1)×12×9
= 4×12×9 = 432m³
Volume of square prism = length×width×height
where;
length = 6m
width = 9m
height = 1 m
Volume = 6×9×1 = 54m³
Therefore the volume of the pool = 432+54 = 486m³
If 4 hours = 2 m up from the deepest part
The volume filled for 4 hours = 1/2×2×12×9 = 108m³
If 4 hours = 108
X hours = 486
make X the subject of formula;
X = 4×486/108
= 1944/108
= 18 hours.
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The function y = 29x2
[tex] y = 29 \times {2}^{x} [/tex]
recursive formula
Answer:
Step-by-step explanation:
[tex]y=29\times2^x\\put~x=x+1\\y1=29\times2^{x+1}=29\times2^x\times2=y\times 2\\y_{n+1} =2y_{n}[/tex]
pls hurry quick!!!!!!!!!!
If the dilation is centered at the origin, the vertices of polygon A′B′C′D′ are: D. A′(−2.4, 3.6), B′(−1.2, 1.2), C′(2.4, −1.2), D′(2.4, 2.4).
What is dilation?In Geometry, dilation refers to a type of transformation which typically changes the size of a geometric object, but not its shape.
Next, we would have to dilate the coordinates of the preimage by using a scale factor of 3/5 centered at the origin as follows:
Ordered pair A (-4, 6) → Ordered pair A' (-4 × 3/5, 6 × 3/5) = Ordered pair A' (-2.4, 3.6).
Ordered pair B (-2, 2) → Ordered pair B' (-2 × 3/5, 2 × 3/5) = Ordered pair B' (-1.2, 1.2).
Ordered pair C (4, -2) → Ordered pair C' (4 × 3/5, -2 × 3/5) = Ordered pair C' (2.4, -1.2).
Ordered pair D (4, 4) → Ordered pair D' (4 × 3/5, 4 × 3/5) = Ordered pair D' (2.4, 2.4).
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URGENT
Please help
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.
P(X≥3), n=7, p=0.1
We can use the binomial probability formula to solve this problem.
P(X≥3) = 1 - P(X<3)
First, we need to find P(X<3), which means finding the probability of getting 0, 1, or 2 successes in 7 trials with a probability of success of 0.1.
P(X<3) = P(X=0) + P(X=1) + P(X=2)
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
P(X=0) = (7 choose 0) * 0.1^0 * 0.9^7 = 0.4783
P(X=1) = (7 choose 1) * 0.1^1 * 0.9^6 = 0.3830
P(X=2) = (7 choose 2) * 0.1^2 * 0.9^5 = 0.1144
P(X<3) = 0.4783 + 0.3830 + 0.1144 = 0.9757
P(X≥3) = 1 - P(X<3) = 1 - 0.9757 = 0.0243
Therefore, the probability of getting at least 3 successes in 7 trials with a probability of success of 0.1 is 0.0243.
Your credit card has a balance of $5400 and an annual interest rate of 12%. You decide to pay off the balance over three years. If there are no further purchases charged to the card, you must pay $179.36 each month, and you will pay a total interest of $1056.96. Assume you decide to pay off the balance over one year rather than three. How much more must you pay each month and how much less will you pay in total interest?
A license plate is to consist of 2 letters followed by 5 digits. Determine the number of different license plates possible if the first letter must be an C, F, J or K and the first digit must be less than 7. Repetition of letters and numbers is not permitted. (Show your work)
There are 6,000,000 different license plates possible given the given conditions of 2 letters followed by 5 Digits, with the first letter being C, F, J, or K, and the first digit being less than 7.
The number of different license plates possible given the given conditions, we need to consider the choices available for each position.
For the first letter, we are given that it must be either C, F, J, or K. So, we have 4 options for the first letter.
For the second letter, any letter can be chosen except the one already used in the first position. Since repetition is not permitted, we have 25 options for the second letter (26 letters in the alphabet minus 1 used in the first position).
For the first digit, it must be less than 7. So, we have 6 options (0, 1, 2, 3, 4, 5).
For the second digit, we have 10 options (0-9).
For the third digit, we also have 10 options.
Similarly, for the fourth and fifth digits, we have 10 options each.
the total number of possible license plates, we need to multiply the number of choices for each position.
Total number of license plates = Number of choices for the first letter * Number of choices for the second letter * Number of choices for the first digit * Number of choices for the second digit * Number of choices for the third digit * Number of choices for the fourth digit * Number of choices for the fifth digit
Total number of license plates = 4 * 25 * 6 * 10 * 10 * 10 * 10 = 6,000,000
Therefore, there are 6,000,000 different license plates possible given the given conditions of 2 letters followed by 5 digits, with the first letter being C, F, J, or K, and the first digit being less than 7.
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What is the constant difference between the consecutive terms
1. 3.5.7.9
Find the standard form of the equation of a circle that has a center at (3, -1) and a point on the circle at (5, 2).
The standard form of the equation of a circle is,
⇒ (x - 3)² + (y + 1)² = 13
Given that;
a circle that has a center at (3, -1) and a point on the circle at (5, 2).
Hence, The value of radius is distance between (3, - 1) and (5, 2).
So, We get;
Radius = √(5 - 3)² + (2 - (- 1))²
Radius = √4 + 9
Radius = √13
So, the standard form of the equation of a circle is,
⇒ (x - 3)² + (y + 1)² = (√13 )²
⇒ (x - 3)² + (y + 1)² = 13
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Help guys I need to answer the questions a. b. c. d. e.
I would appreciate it.
a. The concentration would be 0.5 mg/L at approximately t = 40 hours.
b. The table representing the concentration of the drug in the bloodstream, t hours after administration is shown below.
c. A reasonable domain for this function is t ≥ 0.
d. The patient should receive the next intravenous dose of the drug in order to maintain a concentration above 1 mg/L and below 8 mg/L at t = 1.25 hour.
e. The concentration of the oral drug and the concentration of the intravenous drug would keep increasing over the first 20 hours after it is administered.
How to calculate when the concentration will be 0.5 mg/L?In order to determine the time when the concentration would be 0.5 mg/L, we would substitute the value of the concentration and then solve the quadratic function for time (t);
c(t) = 20t/(t² + 4)
0.5 = 20t/(t² + 4)
0.5(t² + 4) = 20t
0.5t² + 2 = 20t
0.5t² + 2 - 20t = 0
t² + 4 - 40t = 0
t² - 40t + 4 = 0
Time, t = 38.8998 ≈ 40 hours.
Part b.
In this context, we would complete the table of values at various time (t) as follows;
t 0 2 4 6 8 10 12 14 16 18 20
c(t) 0 5 4 3 2.35 1.92 1.62 1.4 1.23 1.10 1.00
Part c.
Since the concentration of the drug at time, t = 0 is equal to 0 mg/L and the concentration actually never becomes zero (0) for any value of time (t), we can reasonably infer and logically deduce that a reasonable domain for this quadratic function is t ≥ 0 or {0, ∞}.
Part d and e.
Furthermore, the intravenous drug must be administered to the patient between the time interval 1.25 ≤ t ≤ 20 in order to maintain a concentration above 1 mg/L and below 8 mg/L.
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My goodness What is an equation of the line that is perpendicular to y=−2/3x+5 and passes through the point (2, 11) ? Enter your equation in the box.
Answer:
Slope that is perpendicular to y=-2/3x+5: 3/2
y-11=3/2(x-2)
Step-by-step explanation:
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Enter the number that belongs in the green box 11 12 20 please help
The value of the missing angle obtained using the Cosine Formula is 28.2°
The Cosine FormulaThe Cosine Formula can be expressed thus ;
CosB = (a²+c²-b²) / 2ac
b = 11
a = 12
c = 20
Substituting the values into the equation
CosB = (12² + 20² - 11²) / 2(12×20)
CosB = (144-400-121)/480
CosB = 423/480
CosB = 0.88125
B =
[tex] {Cos}^{ - 1} (0.88125)[/tex]
B = 28.2°
Therefore, the value of the missing angle is 28.2°
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Solve for n. n/n_1 +2/n+1 =2
Answer:
Step-by-step explanation:
[tex]\frac{n}{n-1}+\frac{2}{n+1} = 2\\\frac{n^2+n + 2n-2}{n^2-1} = 2\\ n^2+3n-2 = 2n^2-2\\n^2=3n\\n^2-3n= 0\\n(n-3) = 0\\n = 0 \\or\\ n = 3[/tex]
A(n) __________ is a compound inequality in which the two simple inequalities are separated by the word “AND.
A(n) "conjunction" is a compound inequality in which the two simple inequalities are separated by the word "AND."
Conjunctions are used in mathematics to represent the intersection of two sets, which means that the solution to the inequality must satisfy both conditions simultaneously.
For example, if we have the inequality 3x + 2 > 7 AND 5x - 3 < 17, the solution must satisfy both 3x + 2 > 7 and 5x - 3 < 17. To solve this type of inequality,
we can use algebraic methods such as isolating the variable in each simple inequality and then finding the intersection of the resulting intervals. Conjunctions are important in many areas of mathematics and are commonly used in algebra, geometry, and calculus.
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aaaaaaahhhhhhh my brain hurts aaaaaaahhhhhhh i cant comprehend!!!!!
Answer:
x=68
Step-by-step explanation:
<ABD = 116 degrees
<ABC = x
<BDC = 48 degrees
<ABD = <ABC + <BDC
116 = x + 48 Subtract 48
x = 116 - 48
x = 68
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