The difference between consecutive integral squares must be greater than 1000. (x+1)^2-x^2>=1000, so x>=999/2 implies x>=500. x=500 does not work, so x>500. Let n=x-500. The sum of the square of n and a number a little over 1000 must result in a new perfect square. By inspection, n^2 should end in a number close to but less than 1000 such that there exists 1000N within the difference of the two squares. Examine when n^2=1000. Then, n=10sqrt(10). One example way to estimate sqrt(10) follows.
3^2=9, so 10=(x+3)^2=x^2+6x+9. x^2 is small, so 10=6x+9. x=1/6 implies sqrt(10)\approx 19/6. This is 3.16.
Then, n approx 31.6. n^2<1000, so n could be 31. Add 500 to get the first square and 501 to get the second. Then, the two integral squares are 531^2 and 532^2. Checking, 531^2=281961 and 532^2=283024. 282,000 straddles the two squares, which have a difference of 1063. The difference has been minimized, so N is minimized N=282000 implies 282
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Someone please help me! What’s the answer??
Answer:
Step-by-step explanation:
its 2
a local eat- in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. the owner of the store has determined that home delivery will be successful if the average time spent on the deliveries does not exceed 36 minutes. the owner has randomly selected 21 customers and has delivered pizzas to their homes in order to test if the mean delivery time actually exceeds 36 minutes. suppose the p-value for the test was found to be .0277.
By using p-value hypothesis test,we find that the mean delivery time actually exceeds 34 minutes.
what is p-value hypothesis test?It is a number calculated from a statistical test that describes how you are found a particular set of observation ,if the null hypothesis were true.P-values are used in hypothesis testing to help to decide whether to reject the null hypothesis .The lower the p-value the greater the statistical significance of observation differences.
what is null and alternate hypothesis?The null hypothesis states that as the assumption that there is no change , no difference and no relationship between two variables.The alternate hypothesis stated that there is a change, difference and relationship between two variables or group.
let we use p-value test
Let u=average time spend on deliveries
so,null hypothesis H0;u[tex]\leq[/tex]34 minutes
alternate hypothesis HA; u >34
Now the decision rule based on the p-value to whether null hypothesis should be accepted or rejected is given by;
.If hypothesis p-value of test statistical is less than the level of significance,then we will our null hypothesis.
.If the p-value of test statistical is more than the level of significance.then we will not reject our null hypothesis.
Here, we assume that the level of significance is 5%.
Since the p-value test statistics is less than the level of significance as 0.029<0.05.
so,we have evidence to reject our null hypothesis.
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A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally, 65 seniors reported using drugs or alcohol within the past month, while 61 national seniors reported using them. Conduct a hypothesis test at the 5% level.
NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
There is evidence to claim that the proportion of drug and alcohol use is higher locally than nationally.
Given that a recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent.
Let p1 be the proportion of local seniors and p2 national seniors.
H₀ : p₁ = p₂
Hₐ : p₁ > p₂
(right tailed test at 5% significance level)
Group I II
Success 69 60 129
Total 100 100 200
p 0.69 0.6 0.645
q 0.31 0.4 0.355
se 0.046249324 0.048989795 0.033836002
p diff 0.09
Std error 0.03384
Z 2.659574468 0
p 0.00391
we find that p value is 0.00391 < 0.05
Hence we reject null hypothesis. There is evidence to claim that the proportion of drug and alcohol use is higher locally than nationally.
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18. In a sample of seven cars, each car was tested for nitrogen-oxide emissions (in grams per mile)
and the following results were obtained: 0.06, 0.11, 0.16, 0.15, 0.14, 0.08, 0.15. Assuming that
this sample is representative of the cars in use, construct a 98% confidence interval estimate of
the mean amount of nitrogen-oxide emissions for all cars. If the EPA requires that nitrogen-oxide
emissions be less than 0.165 g/mi, can we safely conclude that this requirement is being met?
Assume the population is normally distributed.
We cannot safely conclude that this requirement is being met because 0.165 is contained in the confidence interval.
What is Normally distribution?
A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.
results obtained are 0.06, 0.11, 0.16, 0.15, 0.14, 0.08, 0.15
[tex]\overline {X} = \frac{0.06 + 0.11 + 0.16 + 0.15 + 0.14 + 0.08 + 0.15}{7}\\\\ \overline {X} = 0.1214\\[/tex]
[tex]S=\sqrt[2]{\frac{0.0091}{n-1} } \\\\S= \sqrt[2]{\frac{0.0091}{7-1} }\\\\S=0.039\\\\n-1 = 6\\\\E= 3.143 * \frac{0.039}{\sqrt[2]{7} } \\\\E= 0.0462\\\\[/tex]
The confidence interval ⇾ 0.0752 < µ < 0.1676
We cannot safely conclude that this requirement is being met because 0.165 is contained in the confidence interval.
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using the geometry of the features from question 1, from what direction did the continental glacier advance (originate)? glaciers generally advanced from the direction where the contour lines on the landforms are closest together (steep slope) toward the direction where the contour lines on the landforms are farther apart (gentle slope).
Continental glacier ice flows from the region where it is thickest toward the edges where it is thinner. In the central thickest parts, the ice flows almost vertically down toward the base, while at the edges of the glacier, it flows horizontally out toward the margins.
Glaciers generally advanced from the direction where the contour lines on the landforms are closest together (steep slope) toward the direction where the contour lines on the landforms are farther apart (gentle slope).
A continental glacier originating in far Northern Canada began to move South towards the Northeastern United States. The ice sheet crept slowly forward, scraping off the loose rock materials and gouging the bedrock beneath the ice as it advanced.
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what is the simplify to 80√
Answer:
Square Root of 80 in Radical Form: 4√5.
Step-by-step explanation:
√80 = 4√5. Meaning that the square root of 80 in radical form 4 √ 5.
OR Decimal form: 8.944
(Not sure if you wanted it in radical form... I also included it in decimal form)
A principal of 3600 was invested in 5.74% interest
Find nth derivative of sin5x.cos2x
Step-by-step explanation:
1/2×2 sin 5x. cosx
=1/2×sin (5x+x)+cos (5x-x)
=1/2 sin 6x +sin 4x
decide if the events are mutually exclusive. explain your reasoning based on a venn diagram. event a: randomly rolling greater than 3 with a six-sided die. event b: randomly rolling less than 5 with a six-sided die.
Analyzing the events a and b given in the question , the events are not mutually exclusive events, which are also called intersecting events in terms of venn diagram.
What is mutually exclusive event?Events that do not take place at the same time are said to be mutually exclusive. For instance, if a coin is tossed, the outcome will either be head or tail; we cannot obtain both outcomes. Since they do not occur at the same time, such occurrences are also known as disjunct events. The probability of an occurrence if A and B are mutually exclusive is indicated by P(A Or B) or P. (A U B).
What is mutually inclusive or intersecting event?Mutually inclusive events permit the occurrence of both occurrences simultaneously or inside a single trial. It refers to events that are required to take place simultaneously by a rule or a natural law. When two occurrences are mutually inclusive, they cannot happen separately.
Here, the events a and b can occur simultaneously, since we can get a number greater than 3 and less than 5 at the same time while rolling a dice randomly.
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Solve:
3250/156 = y/40
Answer:
y = 833.(3) .3 repeatingStep-by-step explanation:
the fraction is a division, we solve with an equation
3250 : 156 = y : 40
y = 3250 × 40 : 156
y = 833.(3) 3 repeating
--------------------------
check
3250 : 156 = 833.(3) : 40
20,83333333333333 = 20,83333333333333
the answer is good
A chocolate chip cookie recipe calls for 2 3/4 cups of flour. You only have a 1/4 - cup measuring cup and a 3/4 - cup that you can use.
a. What are different combinations of the measuring cups that you can use to get a total of 2 3/4 cups of flour?
Answer:
Step-by-step explanation:
You could use 1 3/4's of a cup and 8 1/4's of a cup.
1 of the 3/4 cups is 3/4 so that covers the 3/4 of the cups of how much flour is needed.
8 of the 1/4 cups is 8/4 which is equal to 2 so that covers the rest of the flour needed.
And 2 + 3/4 is 2 3/4 which is the amount of flour that is needed.
OR
You could use 3 3/4's of a cup and 2 1/4's of a cup.
3/4 + 1/4=4/4
3/4+1/4=4/4
4/4 + 4/4 is the same thing as 1+1 which is 2, so that covers the 2 cups of the flour that is needed, and then you add another 3/4, now you have
2 3/4, which is the amount of flour needed.
(I think that there might be other ways/combinations but I only included 2..)
What is the x-intercept of 4x+2y=6?
Ashley 1/2 package of raisins for a fruit cake. she then uses 1/9 of the remainder for muffins. what fraction of the package of raisins does she have left?..
The fraction of the package of raisins Ashley left with will be equal to 7/18.
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.
They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.
As per the given information in the question,
Amount of raisins used for fruit cake = 1/2
Amount of raisins used for muffins = 1/9
Then, the amount of raisins left will be,
1 - (1/2 + 1/9)
= [18 - (9 + 2)]/18
= (18 - 11)/18
= 7/18
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Find the x-intercept of the line 3x + 19y = -18
Answer:
Step-by-step explanation:
Suppose the diameter of a circle is 16 units. What is its circumference?
Use 3.14 for π and enter your answer as a decimal.
Answer: 50.24
Step-by-step explanation:
The formula to find the circumference of a circle is two pi r. So we just have substituted value into our formula. So we have To multiply by pi, so let's use 3.14 multiplied by our sequence to eight, so this is equal to 16, multiply by 3.14, which is equal to 50.24.
consider the following hypotheses that relate to the medical field: h0: a person is free of disease. ha: a person has disease. in this instance, a type i error is often referred to as . multiple choice
This hypothesis is a false positive.
What is a false positive result?
When a scientist concludes something is real when it is actually wrong, this is known as a false positive (also called a type I error). A "false alarm" is a false positive. Saying something is false when it is truly true is known as a false negative (also called a type II error). A false negative indicates that something was missed or that something that was present was not discovered.
A false positive is getting a positive result that should be negative (this is also known as a “type I error”). A false negative is getting a negative result that should be positive (this is also known as a “type II error”).
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The data below consist of 25 samples of 4 observations each on the lengths of particular bolts manufactured for use in a large aircraft. The target length of these bolts is 37 centimeters. Answer the below questions and show all hand written, SPSS (screenshots) or excel work.
a) Is the process in statistical control?
b) If not in statistical control, why? Explain.
c) Given that the tolerance of these bolts is + .01 centimeters, determine the
i. Cp
ii. CpK values of this process and the
iii. Sigma level Samples
Samples
Sub 1
Sub 2
Sub 3
Sub 4
1
36.99
37.02
37.04
37.01
2
37.01
37.04
37.03
36.98
3
36.98
37.03
37.03
36.99
4
37.00
37.00
37.00
36.98
5
36.98
36.99
36.99
36.96
6
36.99
36.96
36.94
36.97
7
36.98
36.97
37.01
36.96
8
36.93
36.96
36.96
36.93
9
36.91
36.99
36.95
36.92
10
36.97
36.99
36.95
36.94
11
37.05
37.05
37.05
37.05
12
37.00
37.04
37.11
37.05
13
37.05
37.04
37.06
37.04
14
37.08
37.08
37.03
37.08
15
37.08
36.99
37.07
37.06
16
36.93
36.99
37.03
37.03
17
37.06
36.94
37.06
36.98
18
36.94
36.96
36.96
37.01
19
37.01
36.98
37.03
37.00
20
37.03
37.07
36.99
37.03
21
36.99
36.99
37.01
37.00
22
37.01
37.00
37.00
36.99
23
37.02
37.00
37.00
37.00
24
37.01
37.01
37.00
37.03
25
36.99
37.00
37.00
36.99
Using the properties of confidence interval and probability we can conclude from the observations that the process is not a statistical control process.
(a) The process is not a statistical process .
b) The control & chart is not in control because there some false alarm at 8-15. There are some special causes in the clata (may be in manufacturing) exist.
(c) (i) Given that Target length = 37 USL + LSL = 37 USL+2SL= 74
and Tolerance = 0.01 USL LSL = 0.01
After Solving equation 1 & 2 we get VSL = 37.005, LSL = 36.995
cp =2 × 0.01 6/0.05 × 2.059 = 0.01 ×0.1457 = 0.0686
(ii) Cp = min (Cpu, CP).
Cpu = 37.005-37 0.073 = 0.06849
CPL = 0.06859
Срк = 2 × 0.06849 = 0.024
The application of statistical methods to monitor and regulate the quality of a manufacturing process is known as SPC (statistical process control) or SQC (statistical quality control).
This increases the efficiency of the process, resulting in more specification-conforming goods with less waste (rework or scrap). SPC can be used to any process that can measure the output of a "compliant product" (a product that fulfils standards).
The primary tools of SPC are run charts, control charts, a focus on continuous improvement, and experiment design. Manufacturing lines are one example of a process that employs SPC.
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10. use a taylor series to approximate the value of the defnite integral. use as many terms as needed to ensure that the error is less than show at least 8 decimal places in your answer.
∛8.1 = 2.00829885025 it has accuracy up to 6 places which means the error is less than at least 8 decimal places .
For example ,
Using the first three terms of the Taylor series expansion of
f(x)=∛x centered at
x = 8, approximate inmate ∛8.1 :
f(x) = ∛x≈2 + (x-8) / 12 - (x-8)² / 288
the first three terms shown will be sufficient to provide a good approximation for ∛x . Evaluating this sum at x = 8.1 gives an approximation for ∛8.1
f(8.1) = ∛8.1 ≈2 + (8.1 -8)/ 12 - (8.1 - 8 )² / 288
= 2.00829861111
∛8.1 = 2.00829885025
With just three terms, the formula above was able to find the approximate accuracy in ∛8.1 to six decimal places .
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Use the determinant function det(A) and rank function rank(A) to determine whether or not the following vectors are linearly dependent.
(a) (2, 4, 5, -3), (-3, 2, 7, 0), (9, 2, 4, 6), (3, 2, -6, 5)
(b) (1, -1, 3, 2), (-1, 2, 4, -5), (3, -4, 2, 9), (7, 2, 1, 3)
(a) Determinant: det(A) = -18; Rank: rank(A) = 4. The determinant and rank are non-zero, so the vectors are linearly independent.(b) Determinant: det(A) = 0; Rank: rank(A) = 3. The determinant is zero and the rank is less than 4, so the vectors are linearly dependent.
(a)
2 4 5 -3
-3 2 7 0
9 2 4 6
3 2 -6 5
Det = -18
(b)
1 -1 3 2
-1 2 4 -5
3 -4 2 9
7 2 1 3
Det = 0
The determinant and rank of the vectors can be used to determine whether or not they are linearly dependent. If the determinant is non-zero and the rank is equal to the number of vectors, then the vectors are linearly independent. If the determinant is zero and the rank is less than the number of vectors, then the vectors are linearly dependent.
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Simplify ( 7x+5y)^3–(7x–5y)^3–30y(7x+5y)(7x–5y)^3
Answer:
-72030x⁴y +18750y⁵ +102900x³y² -52500xy⁴ +1470x²y +250y³
Step-by-step explanation:
You want to simplify (7x+5y)^3–(7x–5y)^3–30y(7x+5y)(7x–5y)^3.
SubstitutionsWe recognize that there are some repeated expressions here that may make it easier to simplify this without multiplying it all out.
Let a = 7x+5y, b = 7x -5y. Then the expression becomes ...
a³ -b³ -30y·a·b³
= (a³ -b³) -30yb²(ab)
= (a -b)(a² +ab +b²) -30yb²·ab
Now ...
a -b = (7x +5y) -(7x -5y) = 10y
a² +b² +ab = (7x +5y)² +(7x -5y)² +(7x +5y)(7x -5y)
= (7x)² +2(7x)(5y) +(5y)² +(7x)² -2(7x)(5y) +(5y)² +(7x)² -(5y)²
= 3(7x)² +(5y)² = 147x² +25y²
So the first pair of terms expands to ...
a³ -b³ = 10y(147x² +25y²) = 1470x²y +250y³
The last term becomes (with a positive sign) ...
30yb²(ab) = 30y(7x -5y)²((7x)² -(5y)²)
= 30y((7x)² -2(7x)(5y) +(5y)²)((7x)² -(5y)²) . . . . see comment below
= 30y((7x)⁴ -(5y)⁴ -70xy((7x)² -(5y)²))
= 72030x⁴y -18750y⁵ -102900x³y² +52500xy⁴
Simplified expression
Putting it all together gives ...
= -72030x⁴y +18750y⁵ +102900x³y² -52500xy⁴ +1470x²y +250y³
__
Additional comment
The difference of squares form is used several times here:
p² -q² = (p -q)(p +q)
The expression ((7x)² -2(7x)(5y) +(5y)²)((7x)² -(5y)²) is decomposed to ...
((7x)² +(5y)²)·((7x)² -(5y)²) - 2(7x)(5y)((7x)² -(5y)²)
This lets us use the difference of squares form to simplify at least part of the expression. This whole thing gets multiplied by -30y.
A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet. 12f 3 ft 31 (a) if water is being pumped into the trough at 2 cubic feet per minute, how fast is the water level rising when h is 1.2 feet deep? X ft/min (b) if the water is rising at a rate of 3/8 inch per minute when h - 2.3, determine the rate at which water is being pumped into the trough fo/min
Therefore ,the water level is rising by 0.1388 ft/min when h is 1.2 feet deep and the water is being pumped at rate of 0.8625 cubic feet per min when water is rising at 3/8 inch/min
What is volume?A three-dimensional space's occupied volume is measured. It is typically quantified using a variety of imperial or US-standard units as well as SI-derived units. The concept of length and volume are related.
Here,
Given: A trough has a 12 foot length and a 3 foot top width. Three-foot-high isosceles triangles make up its ends. 12f 3 ft 31
So the first case:
using this we find the rate of Volume,
So,
=> dV/dt = length * height *dh/dt
=> dV/dt = 12 * 1.2 *dh/dt
=> 2 = 12*1.2* dh/dt
=> 2 = 14.4 * dh/dt
=>dh/dt = 2/14.4
=>dh/dt = 0.1388 ft/min
Therefore ,the water level is rising by 0.1388 ft/min when h is 1.2 feet deep .
Second case:
Since water level is rising by 3/8 inch per min =0.03125 feet/min
=> dV/dt = length * height *dh/dt
=> dV/dt = 12 * 2.3 *0.03125
=>dV/dt = 0.8625 cubic feet per min
Therefore , the water is being pumped at rate of 0.8625 cubic feet per min.
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4. Kaya ran 1 2/5miles on Monday and 2 1/3 miles on
Tuesday. What was the total distance, in miles, Kaya
ran during those 2 days?
Answer: 3 11/15 please mark brainliest If I helped you.
the question is kayar and 12 by 5 miles on Monday and 21 by three miles on Tuesday what is the total distance in miles kayuren during those two days first phone on Monday how much run that was 12 by 5 miles on Tuesday Shirin to 1 by 3 minus now this whole part and fractional part are written separately so this can be converted into a mixed fraction like when a number is of the form of p by see that is one whole number and fraction then it is written as a + b by c so we can write Monday that was 12 by 5 miles that is
12 by 1 + 2 by 5 that will be 5 will be LCM of 5 + 2 will be 7 by 5 MI and Tuesday it will be 21 by 3 that is 2 + 1 by 3 3 will be the LCM of 3 and 22 will be 6 plus one that is 7 by 3 minus in question is asked that what was the total distance kayar and thus during today's so Monday plus Tuesday will be the total total 27 by 5 + 7 by 3 that will be equal to LCM will be 15 this will be X 307 into 3 + 7 and 25 that
is 21 + 45 upon 15 that will be equal to 56 upon 15 Now since we have to give answer in mixed fraction in whole number and fraction this a bi bi can be divided into a whole number and fraction part when divided by be the remainder is remainder is written here b is written here and question is written here so 56 by 15 can be written as 15 and 23 is 45 three years question remainder will be 11:00 that is 56 - 45 and below will be the denominator will be 15 so this is our answer and the correct
Trina is 54 3 4 inches tall. Morgan is 1 1 2 inches taller than Trina and Jane is 1 1 5 inches taller than Morgan. How tall is Jane? Label the names on the tape diagram to represent this problem. Three tape diagrams, one below the other. The first tape diagram is the shortest. The third tape diagram is the longest. Trina Morgan Jane Great job! Label the tape diagram to represent this problem. Three tape diagrams, one below the other. The first tape diagram is the shortest. The third tape diagram is the longest. The second tape diagram is longer than the first and shorter than the third tape diagram. A bracket covers the length of the first tape diagram. A bracket covers the increased length of the second tape diagram compared to the first tape diagram. A bracket covers the increased length of the third tape diagram compared to the second tape diagram. A bracket covers the entire length of the third tape diagram. 54 3 4 1 1 2 1 1 5 ? TrinaMorganJane Good work!
The height of Jane will be 38 9/30 inches.
What is Addition?The process of combining two or more numbers is called the Addition.
Given that;
Trina is 54 3/4 inches tall. Morgan is 1 1/2 inches taller than Trina and Jane is 1 1/5 inches taller than Morgan.
Now,
Since, Trina is 54 3/4 inches tall.
And, Morgan is 1 1/2 inches taller than Trina.
Hence, The height of Morgan = 54 3/4 + 1 1/2
= 219/4 + 3/2
= 219/4 + 6/4
= 225/4
And, Jane is 1 1/5 inches taller than Morgan.
Hence, The height of Jane = 225/4 + 1 1/5
= 225/4 + 6/5
= (1125 + 24)/30
= 1149/30
Thus, The height of Jane = 38 9/30 inches
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use lagrange multipliers to find the maximum or minimum values of the function subject to the given constraint. (if an answer does not exist, enter dne.) f(x, y, z)
To determine the maximum or minimum value of a given function, Lagrange multipliers are used.
What is langrange multipliers?
Let's set up everything now. We want to optimize (i.e., find the minimum and maximum value of) a function, f, under the condition that g (x, y, and z) = k. (x, y, and z). Once more, the equation that describes the boundary of a region may or may not be the constraint. Although the process is actually quite simple, there are times when the workload seems quite overwhelming.
Solve the following system of equations.
∇f(x,y,z) = λ
∇g(x,y,z)
g(x,y,z)= k
If there are minimum and maximum values, enter them into f(x,y,z) along with all of the solutions (x,y,z) from the first step.
∇ g ≠ → 0 at the point.
The constant, λ, is called the Lagrange Multiplier.
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If f(x) = -3x-2, find f(3)
Answer:
-11
Step-by-step explanation:
To find f(3), we simply need to plug 3 in for x in the function f(x) = -3x-2. This gives us:
f(3) = -3(3) - 2 = -9 - 2 = -11
Therefore, the value of f(3) is -11.
if a rectangle and a square have the same perimeter then which one will have a larger area
Answer:
The area of the square is larger than the area of the rectangular field.
what is 70x+10=200 pretty pls help
Answer: 19/7
Step-by-step explanation:
Your goal is to isolate x or get x by itself.
Move all other variables to the opposite side.
70x+10-10=200-10
70x=190
Divide both sides by 70
x= 19/7
Answer:
[tex]x= \frac{19}{7}[/tex] OR [tex]2 \frac{5}{7}[/tex]
Step-by-step explanation:
To do this you need to:
1. Subtract 10 from both sides {As shown below}
[tex]70x+10-10=200-10[/tex]
2. Simplify {As shown below}
[tex]70x=190[/tex]
3. Divide both sides by the same factor {As shown below}
[tex]\frac{70x}{70} = \frac{190}{70}[/tex]
4. Simplify {As shown below}
{a. Cancel terms that are in both the numerator and the denominator}
{b. Divide the numbers}
[tex]x= \frac{19}{7}[/tex] OR [tex]2 \frac{5}{7}[/tex]
{Please give Brainliest}
Identify the slope of the line and the slopes of any parallel and perpendicular lines y=-1/2x+2
Answer:
Slope of the line, [tex]m_{1} = -\frac{1}{2}[/tex]
Slope of parallel line, same as the slope above
Slope of perpendicular line, [tex]m_{2} = 2[/tex]
Step-by-step explanation:
Parallel line: [tex]m_{1} = m_{2}[/tex]
Perpendicular line: [tex]m_{1} * m_{2} = -1[/tex]
[tex]y = mx +b[/tex]
Where, m = slope
Thus, in the equation provided, the slope is [tex]-\frac{1}{2}[/tex]
Finding the slope of perpendicular line:
[tex]m_{1} * m_{2} = -1\\m_{2} = \frac{-1}{m_{1}}\\m_{2} = -1 * -2\\m_{2} = 2[/tex]
Select the choice that shows the first step in finding 3,584÷7 using the standard algorithm.
Answer:
You did not provide the choices, but the first step to find the result of the operation using standard algorithm is to set up a long division
find the magnitude and direction angle of the following vector. Write your angle in degrees rounded to four decimal places. u = 2i + 8j nswer 4 Points ecall that answers entered in degrees will require a degree symbol, which is located in the keypad. ||u|| = 0 =
The magnitude of vector is 8.24 and angle is 75.9638.
What is vector?
A vector could be a amount that not solely describes the magnitude however additionally describes the movement of an object or the position of an object with reference to another purpose or object.
Main body:
we know that the magnitude of vector is found out by,
| u | = [tex]\sqrt{i^{2}+j^{2} }[/tex]
so here , u = 2i + 8j
|u| = [tex]\sqrt{2^{2} +8^{2} }[/tex]
|u| = [tex]\sqrt{68}[/tex]
|u| = 8.24
now to find the direction , angle
tan∅ = j/k
tan∅ = 8/2
∅ = tan⁻¹ (4)
∅ = 75.9638°
Hence , direction angle of the following vector is ∅ = 75.9638°
to know more about vector , visit:
https://brainly.com/question/25705666
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