The first negative term of the sequence is -2
How to find the terms of a sequence?The terms of the sequence which is the first negative term can be calculated as follows:
The sequence with nth term is 150 - 4n.
The first negative term will be the first term you will multiply by 4 that will be greater than 150.
Therefore,
nth term with first negative number = 150 - 4(38)
nth term with first negative number = 150 - 152
nth term with first negative number = -2
Therefore, the first negative term of the sequence is -2
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A summer camp cookout is planned for the campers and their families. there is room for 450 people. each adult costs $7, and each camper costs $4. there is a maximum budget of $1,150. write the system of inequalities to represent this real-world scenario, where x is the number of adults and y is the number of campers. x y ≤ 1,150 7x 4y ≤ 450 x y ≤ 450 7x 4y ≤ 1,150 x y ≤ 1,150 4x 7y ≤ 450 x y ≤ 450 4x 7y ≤ 1,150
Hence, the required inequality is x+y≤4, 7x+4y≤1150
What is inequality?inequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
How to solve?Let x be the number of adults and y be the number of campers.
There are rooms for 450 people, so
x+y≤450.
Each adult costs $7, then x adults cost $7x.
Each camper costs $4, then y campers cost $4y.
There is a maximum budget of $1,150, so
7x+4y≤1,150
Hence, you get the system of two inequalities:
x+y≤4
7x+4y≤1150
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Answer:
x + y [tex]\leq[/tex] 450
7x + 4y [tex]\leq[/tex] 1,150
Step-by-step explanation:
X and Y is the amount of people it can fit.
7 and 4 is the amount of money for each person.
7x is the amount per adult, 4y is the amount per camper.
Hope this helps.
Use the function below to find F(1)
Answer:
[tex]B: \frac{1}{2}[/tex]
Step-by-step explanation:
Plug 1 in as t
[tex]F(1) = 4 * \frac{1}{2^{3(1)}}[/tex]
Simplify the exponent 3*1
[tex]F(1) = 4 * \frac{1}{2^{3}}[/tex]
Cube the 2
[tex]F(1) = 4 * \frac{1}{8}[/tex]
Multiply:
[tex]F(1) = \frac{4}{8}[/tex]
Simplify:
[tex]F(1)=\frac{1}{2}[/tex]
the mean value of land and buildings per acre from a sample of farms is $1400 with a standard deviation of $300 the data set has a bell shaped distribution assume the number of farms in the sample is 72 use empirical rule to estimate the number of farms whose land and building values per acre are between $1100 and $1700
Using the Empirical Rule, it is found that 49 farms in the sample have land and building values per acre between $1100 and $1700.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.Considering the given mean and standard deviation, values between $1100 and $1700 are within 1 standard deviation of the mean, which is a percentage of 68%.
Hence, the number of farms out of 72 is:
0.68 x 72 = 49 farms.
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1. (y + x) = 4; use x = 2 and y = 2
2. x + y ÷ 6; use x = 5 and y = 6
3. y(x + 5); use x = 1 and y = 4
4. q-m+q; use m = 3 and q = 6
Step-by-step explanation:
1-)2+2=4
2-)5+6÷6=6
3-)4(1+5)=24
4-)6-3+6=9
A ______ of two linear _______ can have one solution, an infinite number of solutions, or no solution.
Answer:
system
equations
Step-by-step explanation:
Answer:
A system of two linear equations can have one solution, an infinite number of solutions, or no solution.
===================================================
Explanation:
An equation is something like [tex]\text{y} = 2\text{x}+5[/tex] and [tex]\text{y} = 3\text{x}+7[/tex]
When we combine two such equations to form a group (of sorts), we consider this to be a system of equations.
We use a single curly brace to write the system
[tex]\begin{cases}\text{y} = 2\text{x}+5\\\text{y} = 3\text{x}+7\end{cases}[/tex]
Here are the three cases mentioned when it comes to solutions.
If the two lines intersect at exactly one point, then the system has exactly one solution. This system is consistent and independent.If the two lines are the same, they intersect at infinitely many points along that line. One line perfectly overlaps the other. Therefore, this scenario leads to infinitely many solutions. The system is dependent because one line depends on the other (since they are one in the same). This system is also consistent because it has at least one solution. Lastly, if the two lines are parallel, then they never cross. The lack of crossing points means there aren't any solutions. We call this an inconsistent system.Side note: Any solution is of the form (x,y)
Which of the following models the context "A plumber who charges $50 for a
house call and $85 per hour"?
Answer:
a. y = 85x + 50
Step-by-step explanation:
a. y = 85x + 50
The surface area of a cone with radius r units and slant height s units is shown below:
30 points
Surface area = 3.14(rs + r2)
Part A: If r = 3 units and s = 5 units, write an expression that can be used to calculate the surface area of the cone. (4 points)
Part B: What is the surface area of the cone? Show your work. (6 points)
Step-by-step explanation:
part A:
[tex]Area_{_{surface}}=3.14*(3*5+3^2);[/tex]
part B:
[tex]Area_{_{surface}}=3.14*(15+9)=3.14*24=75.36[units^2].[/tex]
Select the equation of the line that passes through the point (–2, 1) and has slope 3 in point-slope form.
(x – 2) = 3(y + 1)
(y + 1) = 3(x – 2)
(y – 1) = 3(x + 2)
(x + 2) = 3(y – 1)
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Select the equation that passes through (-2,1) and has slope 3
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
Formula used, here [tex]\bf{y-y1=m(x-x1)}[/tex]
[tex]\bf{y-1=3(x-(-2)}[/tex] | put in the values, then, simplify
[tex]\bf{y-1=3(x+2)}[/tex]
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=y-1=3(x+2)}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic \not1\theta l}}[/tex]
∞
Identity the x-intercept of the liner equation 3x + y -9=0
Answer:
The x intercept is 3
(3,0)
Step-by-step explanation:
3x+y -9 =0
To find the x intercept, set y=9 and solve for x.
3x+0-9=0
3x -9=0
Add 9 to each side
3x-9+9=9
3x =9
Divide by 3
3x/3 = 9/3
x =3
The x intercept is 3
(3,0)
How many solutions exist for the system of equations in the graph?
Answer:
Two
Step-by-step explanation:
Solutions are when the two graphs intersect
If the width of the dining room table is w feet, and the length is 3w - 2 feet, write an
algebraic expression that represents the perimeter of the table.
Answer:
2(w)+2(3w-2), or, 8w-4Step-by-step explanation:
The formula for finding the perimeter is 2w+2L (2*width + 2*length)
So, since we know the width is "w" and the length is "3w-2", we can just substitute those into the equation.
2(w)+2(3w-2)
From there, if needed, you can simplify to:
2w + 6w-4
Add like terms:
8w - 4
Hope that helps.
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Using the transformation T: (x, y) (x + 2, y + 1), find the distance named.
Triangle ABC was translated using the rule (x, y) (x + 2, y + 1) to form congruent triangle A'B'C' with AA' = √5 units
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
Point A is at (0, 0). Using the transformation T: (x, y) (x + 2, y + 1), point A' = (2, 1). Hence:
[tex]AA'=\sqrt{(1-0)^2+(2 - 0)^2}=\sqrt{5}[/tex]
Triangle ABC was translated using the rule (x, y) (x + 2, y + 1) to form congruent triangle A'B'C' with AA' = √5 units
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pleasee help!!!!
20 points
The function with the same end behavior of f(x) is the last option:
[tex]g(x) = (-\frac{1}{3} )*x[/tex]
Which function has the same end behavior of f(x)?
By looking at the graph, we can see that the end behavior of f(x) is:
as x → ∞; f(x) → -∞
as x → -∞; f(x) → ∞
Then we just want a function that depends linearly with x and that has a negative coefficient.
The correct option is the last one:
[tex]g(x) = (-\frac{1}{3} )*x[/tex]
Where clearly, when x tends to infinity the function tends to negative infinity, and when x tends to negative infinity, the function tends to infinity.
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A student hypothesized that in the US adult population, women drank the same amount of water per day as men per kg of body weight as the null hypothesis. The probability value for her null hypothesis was 0.02. Assume the alpha level was 0.05. Which conclusion is justified?
The conclusion that is justified based on the research is that he rejected the null hypothesis that women drank the same amount of water per kg of body weight per day as men.
How to illustrate the research?It should be noted that a research is simply used to get information about a topic.
In this case, it can be deduced that a type 1 error is committed. This implies the rejection of the null hypothesis when it's true.
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Which of the following is equivalent to 6^2/5
Where are the options?
IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual.Find the probability that the person has an IQ score between 92 and 108.
Using the normal distribution, it is found that there is a 0.4038 = 40.38% probability that the person has an IQ score between 92 and 108.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 100, \sigma = 15[/tex].
The probability that the person has an IQ score between 92 and 108 is the p-value of Z when X = 108 subtracted by the p-value of Z when X = 92, hence:
X = 108:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{108 - 100}{15}[/tex]
Z = 0.53
Z = 0.53 has a p-value of 0.7019.
X = 92:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{92 - 100}{15}[/tex]
Z = -0.53
Z = -0.53 has a p-value of 0.2981.
0.7019 - 0.2981 = 0.4038.
0.4038 = 40.38% probability that the person has an IQ score between 92 and 108.
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I need help please. Trying to get my HS diploma. I did not graduate :(
Which of the following is the graph of f(x)+1?
The graph of f(x) + 1 is the graph in the option C.
Which is the graph of f(x) + 1?
For a given function f(x), a vertical translation is written as:
g(x) = f(x) + N
If N > 0, then the translation is upwards.If N < 0, then the translation is downwards.Here we have g(x) = f(x) + 1, so we have a translation of 1 unit upwards, the graph of f(x) + 1 is the graph of f(x) but translated one unit upwards.
From that, we conclude that the correct option is C.
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Find a polynomial function of degree 5 with -3 as a zero of multiplicity 3, 0 as a zero of multiplicity 1, and 3 as a zero of multiplicity 1.
[tex](x+3)^3\cdot x\cdot (x-3)=(x^3+9x^2+27x+27)\cdot (x^2-3x)=\\=x^5-3x^4+9x^4-27x^3+27x^3-81x^2+27x^2-81x=\\=x^5+6x^4-54x^2-81x[/tex]
The equation 5x2 30x 15 = 0 is being rewritten in vertex form. fill in the missing step. given 5x2 30x 15 = 0 step 1 ✔ step 2 5(x2 6x 9) 15 − 45 = 0 step 3 5(x 3)2 − 30 = 0 5(x2 30x ___) 15 ___ = 0 5(x2 30x ___) − 15 ___ = 0 5(x2 6x ___) − 15 ___ = 0 5(x2 6x ___) 15 ___ = 0
The missing step in making the equation in vertex form is option D which is
[tex]5(x^{2} +[/tex]6x____)+15.
Given Equation [tex]5x^{2} +30x+15=0[/tex]
Parabola in vertex form. Equation is a relationship between two or more variables which is expressed in equal to form. It is solved to find the variables.
To express the equation of a parabola in vertex form we must complete squares. The equation is given as
[tex]5x^{2} +30x+15=0[/tex]
The first step is to factor 5 and leave space to complete the third term in the parenthesis, along with a space outside it to compensate. This should look like
([tex]5(x^{2} +6x............)+15..........=0[/tex]
Those spaces need to be filled out like shown in the step 2. Thus the correct step is D.
Hence the correct step in vertex form is D which is
[tex]5(x^{2} +6x[/tex]___-)+15____=0.
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Tony made 14 { L}14 L14, start text, space, L, end text of lemonade for a party. His guests drank 9,500 { mL}9,500 mL9, 500,m, L, end text of the lemonade.
How many milliliters of lemonade did Tony have left over?
Unit conversion is a way of converting some common units into another without changing their real value. The lemonade left with Tony is 4500ml.
What is unit conversion?Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.
One litre is equal to 1000 millilitres. Tony made 14 Liter of lemonade, therefore, Tony made 14,000 millilitres of lemonade. His guest drank 9500 millilitres. Therefore, the lemonade left with Tony is,
Lemonade left = 14,000 - 9,500 = 4,500 ml
Hence, the lemonade left with Tony is 4500ml.
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15 people were asked to measure their pulse rates after completing a 3 km run. The sample data are given below and are assumed to be normally distributed. Use a TI-83, TI-83 plus, or TI-84 calculator to construct a 98% confidence interval for the mean of the population. Round your answers to two decimal places and use increasing order.
Using the t-distribution, the 98% confidence interval for the mean of the population is (99.21, 110.79).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.Researching the problem on the internet, the data-set is given as follows:
104, 102, 103, 105, 125, 106, 107, 110, 110, 95, 108, 86, 112, 101, 101.
The parameters are given as follows:
[tex]\overline{x} = 105, s = 8.54, n = 15[/tex].
The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 15- 1 = 14 df, is t = 2.6245.
Hence the bounds of the interval are:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 105 - 2.6245\frac{8.54}{\sqrt{15}} = 99.21[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 105 + 2.6245\frac{8.54}{\sqrt{15}} = 110.79[/tex]
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After five science tests, Sonya's average score
is 89. If she gets a 95 on the sixth test, what is
her new average?
A. 89.50
B. 89.90
C. 90.00
D. 90.50
Answer:
C
Step-by-step explanation:
The sum of Sonya's 5 initial tests = 89*5 = 445.
445 + 95 = 540 (sum of the 6 tests)
Average = 540/6 = 90
Hence C
Answer:
C. 90.00
Step-by-step explanation:
We find average by adding up all values in a data set and dividing by the total number of values we have
We can say that Sonya got 89 for each test (it doesn't matter what each test score exactly was--you'll see why in a second)
So, we can add up 89 five times (5 tests have occured)
*I say add up, because that's what average is, but you can find this number by multiplying 89 · 5
89 · 5 = 445
(89 + 89 + 89 + 89 + 89 = 445)
Now, we need to add up our new value: 95
445 + 95 = 540
So, we can now divide 540 (sum of all values) by 6 (total number of values)
540 ÷ 6 = 90
So, C (90.00) is her new average
hope this helps! have a lovely day :)
A family has to travel 380 miles to reach their vacation spot. They plan to stop for lunch after driving 2/5 of the distance. How far will they have traveled when they stop for lunch?
Answer:
152 miles
Step-by-step explanation:
380/5 = 76
76*2 = 152
as they will have traveled 2/5, you would need to divide your miles by 5 then multiply by 2!
What is the least
common multiple of 12 and 16?
Answer: 48
Explanation: 16 x 3 = 48, 12 x 4 = 48
Please answer this question
Answer: B
Step-by-step explanation:
The factors of 1 are [tex]\pm 1[/tex]
The factors of 20 are [tex]\pm \{1, 2, 4, 5, 10, 20\}[/tex].
By the rational root theorem, we see that the answer is B.
whats the rule (-2,-7) (0,-1) (7, 22)
The rule of the points is y = 3.2x - 0.7
How to determine the rule?The points are given as:
(-2,-7) (0,-1) (7, 22)
The above points form an approximate linear equation.
So, we make use of a linear regression to determine the rule
When the above points are entered in a statistical calculator, we have the following summary:
Sum of X = 5Sum of Y = 14Mean X = 1.6667Mean Y = 4.6667Sum of squares (SSX) = 44.6667Sum of products (SP) = 144.6667The regression equation is then represented as:
y = bx + a
Where
b = SP/SSX = 144.67/44.67 = 3.23881
a = MY - bMX = 4.67 - (3.24*1.67) = -0.73134
This gives
y = 3.23881x - 0.73134
Approximate
y = 3.2x - 0.7
Hence, the rule of the points is y = 3.2x - 0.7
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On a zip-line course, you are harnessed to a cable that travels through the treetops. You start at Platform B and zip to the other platform. What is the coordinate when you reach half way?
what is the midpoint
The distance from Platform B to Platform C is 26.926 units
The given parameters are;
The zip-line course distance from platform A to platform F is given;
On the given graph of the path of travel we have;
Coordinates of the point B = (-25, -20) and the coordinates of the point C = (-15, 5).
What is the distance formula?
The distance between two points with coordinates (x₁, y₁) and (x₂, y₂) is given by the formula
[tex]l=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
Therefore, the distance between B and C is found by substituting (-25, -20) = (x₁, y₁) and (-15, 5) = (x₂, y₂)
Which gives
[tex]l=\sqrt{(5-(-20))^2}+((-15)-(-25))^2\\l=26.926 units[/tex]
The distance from points B to C = 26.926 units. The distance from Platform B to Platform C is 26.926 units.
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Use the Empirical Rule to determine the percentage of candies with weights between 0.7 and 0.98 gram. Hint: x=0.84
Using the Empirical Rule, it is found that 95% of the candies have weights between 0.7 and 0.98 gram.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.Researching this problem on the internet, we have that:
The mean is of 0.84.The standard deviation is of 0.07.Then 95% of the candies have weights between 0.7 and 0.98 gram, as:
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which of the fallowing is a mononial
Answer:
A monomial is a polynomial, which has only one term. A monomial is an algebraic expression with a single term but can have multiple variables and a higher degree too. For example, 9x3yz is a single term, where 9 is the coefficient, x, y, z are the variables and 3 is the degree of monomial.
Match each problem to its solution 8,8.2,9,56.25
The computation shows that the amount will be:
$56.25.$988.2 poundsHow to compute the values?Jonah earns $12.50 per hour
He works for 4.5 hours
Amount he earned will be:
= 12.50 × 4.5 = $55.25
Items worth is $41.23
Amount paid is $50.23
Extra amount paid will be:
= 50.23 - 41.23
= $9
Length of cloth available is 20 m
Length of one long-sleeved blouse is 2.5m
Number of blouses that can be made will be:
= 20/2.5 = 8
Potatoes weight is 3.2 pounds
Oranges weight is 2.3 pounds
Onions weight is 2.7 pounds
Total weight of the purchase will be:
= 3.2 + 2.3 + 2.7 = 8.2 pounds
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Complete question:
Match each problem to its solution. 8 8.2 9 56.25 Jonah earns $12.50 per hour as a marketing intern. If he works for 4.5 hours, how many dollars does he earn? arrowRight Jessica purchased items worth $41.23 at the local grocery store. The cashier made a mistake while ringing up her items, and Jessica ended up paying $50.23. How many extra dollars did she pay? arrowRight Josie has 20 meters of cloth. She needs to make long-sleeved blouses with that cloth. If one long-sleeved blouse requires 2.5 meters of cloth, how many blouses can she make with the material? arrowRight Jeremy bought 3.2 pounds of potatoes, 2.3 pounds of oranges, and 2.7 pounds of onions. How many pounds does his purchase weigh? arrowRight