Let
width be xLength=x+3ATQ
[tex]\\ \sf \longmapsto Area=Length\times Width[/tex]
[tex]\\ \sf \longmapsto x(x+3)=28[/tex]
[tex]\\ \sf \longmapsto x^2+3x=28[/tex]
[tex]\\ \sf \longmapsto x^2+3x-28=0[/tex]
[tex]\\ \sf \longmapsto x^2+7x-4x-28=0[/tex]
[tex]\\ \sf \longmapsto x(x+7)-4(x+7)=0[/tex]
[tex]\\ \sf \longmapsto (x-4)(x+7)=0[/tex]
[tex]\\ \sf \longmapsto x=4\:or\:x=-7[/tex]
Ignore negative value[tex]\\ \sf \longmapsto Width=4units[/tex]
[tex]\\ \sf \longmapsto Length=4+3=7units[/tex]
Consider the following ordered data. 6 9 9 10 11 11 12 13 14 (a) Find the low, Q1, median, Q3, and high. low Q1 median Q3 high (b) Find the interquartile range.
Answer:
Low Q1 Median Q3 High
6 9 11 12.5 14
The interquartile range = 3.5
Step-by-step explanation:
Given that:
Consider the following ordered data. 6 9 9 10 11 11 12 13 14
From the above dataset, the highest value = 14 and the lowest value = 6
The median is the middle number = 11
For Q1, i.e the median of the lower half
we have the ordered data = 6, 9, 9, 10
here , we have to values as the middle number , n order to determine the median, the mean will be the mean average of the two middle numbers.
i.e
median = [tex]\dfrac{9+9}{2}[/tex]
median = [tex]\dfrac{18}{2}[/tex]
median = 9
Q3, i.e median of the upper half
we have the ordered data = 11 12 13 14
The same use case is applicable here.
Median = [tex]\dfrac{12+13}{2}[/tex]
Median = [tex]\dfrac{25}{2}[/tex]
Median = 12.5
Low Q1 Median Q3 High
6 9 11 12.5 14
The interquartile range = Q3 - Q1
The interquartile range = 12.5 - 9
The interquartile range = 3.5
if b<0 and |b| = 4b+15 what is the value of b
Answer:
|b|= 4b+15
-b=4b+15
-b-4b= 15
-5b= 15
b= 15/-5
b= -3
the ans -3
If [tex]a<0[/tex] the [tex]|a|=-a[/tex]
So
[tex]|b|=4b+15\\-b=4b+15\\5b=-15\\b=-3[/tex]
Is the number 7 included in the following interval: (2,7] *
Answer:
yes number 7 is included in this interval .
............
This solid shape is made from 5 cubes. Which of the diagrams show the plan of the solid? Please help!
Answer:
A Maybe
Step-by-step explanation:
Cogntive identification
Unable to answer mathematically or analytically
The Plan of the solid shape is shown by : (A)
What is the Meaning of solid shape?A solid shape can be defined as a shape that possesses three dimensions. that is to say they are three dimensional shapes.
A solid shape has both length, width and height. They are more tangible and look physical than two dimensional shape.
solid shapes can take up space in the universe because they are more tangible and realistic.
In conclusion, the Plan of the solid shape is shown by : (A)
Learn more about solid shape: https://brainly.com/question/16717260
#SPJ2
Big sleds must hold 3 children and small sleds must hold 2 children. If 17 children want to go sledding at the same time, how many of each type of sled is needed?
Answer:
5 big sleds and 1 small sled
Write an expression to represent: Four less than the product of one and a number xxx
Answer:
xxx-4
Step-by-step explanation:
(1×xxx)-4
yietisyksykd
Answer:
(1xxx)-4
Step-by-step explanation:
Since 1 and xxx are multiplied, they produce 1xxx and eventually 4 is subtracted so 1xxx-4 and I put the brackets just to make it clear about what is going on in the expression
Could anyone help me with this question please? Thank you.
Answer:
C) 549 km²
Step-by-step explanation:
The area of the regular pentagon is given by ...
A = (1/2)Pa
where P represents the perimeter, and 'a' represents the apothem (6.2 km). Of course, the perimeter is 5 times the side length.
The lateral area is the product of the perimeter and the height:
LA = Ph
Using these formulas, and recognizing the total area includes two (2) pentagons, we have ...
total area = (LA) +2(A) = Ph +2(1/2)Pa = P(h +a)
= (45 km)(6 km +6.2 km) = 549 km^2
What is the volume of a sphere, to the nearest cubic inch, if the radius equals 5 inches? Use π = 3.14.
Answer:
V = 523 in^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
V = 4/3 ( 3.14) * 5^3
V = 523.33333repeating
Rounding to the nearest inch^3
V = 523 in^3
Answer:
[tex] 523.6 {in}^{3} [/tex]
Step-by-step explanation:
[tex]v = \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \pi \times 5 \times 5 \times 5 \\ = 523.6 {in}^{3} [/tex]
The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of 7 cm/s. When the length is 12 cm and the width is 5 cm, how fast is the area of the rectangle increasing?
Answer:
129 m/s^2
Step-by-step explanation:
The length of a rectangle is increasing at a rate of 9m/s
dL/dt = 9m/s
The width is increasing at a rate of 7m/s
dw/dt= 7m/s
The formular for solving the area of a rectangle is length × width
Therefore, to calculate how fast the rectangle is increasing we will apply the product rule
dA/dt= L × dw/dt + W × dl/dt
= 12×7 + 5×9
= 84+45
= 129m/s^2
Hence the area of the rectangle is increasing at 129m/s^2
A hypothesis test is to be performed in order to test the proportion of people in a population that have some characteristic of interest. Select all of the pieces of information that are needed in order to calculate the test statistic for the hypothesis test:
No piece of information is supplied to choose from ; However, the requirements for the test statistic of the hypothesis in question is given below.
Answer:
Kindly check explanation
Step-by-step explanation:
The hypothesis in the question above which is to be tested is a one sample proportion test ;
The test statistic formula for a one sample proportion test is given as :
Test statistic = (Phat - P) / √[P(1 - P) / n] ;
Where;
Phat = sample proportion
P = population proportion
n = sample size
Sample proportion = x / n ;
Therefore, once the parameters (Sample proportion, population proportion and sample size are given) then obtaining the test statistic is possible.
Given: x - 5 > -2. Choose the solution set.
Answer: x>3
Step-by-step explanation:
x-5>2
x>+5-2
x>3
All of Ralph’s ranch land was divided equally among his six children whose daughter land portion of the ranch land was divided among her four children how much of Roslyn was in Inherited by 1 of Lynn’s children
Answer: 1/24 of Ralph's land
Step-by-step explanation:
Ralph gave each of his children a 6th of his land.
= 1/6
Lynn being his daughter got 1/6 of his land. She then shared it to her 4 children.
Children got 1/4 of Lynn's land which is 1/6 of Ralph's land.
Lynn's children therefore got;
= 1/4 * 1/6
= 1/24 of the land
17. Complete the following equation using <, >, or =
7 __ 24/2
A. >
B. <
C. =
467,768 round it to
the hundreds place
Answer:
467,800
Step-by-step explanation:
When nearing to the hundred you look at the number 6. It’s greater than 5 so the previous number 7 turns into 8 and the numbers 6 and 8 became 0.
The answer is 467,800
Use any estimation strategy to calculate ,51.12 times 87.906 pls help!
Answer:
the real answer is: 4493.75472
BUT for ESTIMATION STRATEGY it is: 4500
Step-by-step explanation:
Calcule o valor de x nas equações literais: a) 5x – a = x+ 5a b) 4x + 3a = 3x+ 5 c) 2 ( 3x -a ) – 4 ( x- a ) = 3 ( x + a ) d) 2x/5 - (x-2a)/3 = a/2 Resolva as equações fracionárias: a) 3/x + 5/(x+2) = 0 , U = R - {0,-2} b) 7/(x-2) = 5/x , U = R - {0,2} c) 2/(x-3) - 4x/(x²-9) = 7/(x+3) , U = R - {-3,3}
Answer:
1) a) [tex]x = \frac{3}{2}\cdot a[/tex], b) [tex]x = 5-3\cdot a[/tex], c) [tex]x = -a[/tex], d) [tex]x = \frac{5}{2}\cdot a[/tex]
2) a) [tex]x = -\frac{3}{4}[/tex], b) [tex]x = -5[/tex], c) [tex]x = 3[/tex]
Step-by-step explanation:
1) a) [tex]5\cdot x - a = x + 5\cdot a[/tex]
[tex]5\cdot x - x = 5\cdot a + a[/tex]
[tex]4\cdot x = 6\cdot a[/tex]
[tex]x = \frac{3}{2}\cdot a[/tex]
b) [tex]4\cdot x + 3\cdot a = 3\cdot x + 5[/tex]
[tex]4\cdot x - 3\cdot x = 5 - 3\cdot a[/tex]
[tex]x = 5-3\cdot a[/tex]
c) [tex]2\cdot (3\cdot x - a) - 4\cdot (x-a) = 3\cdot (x+a)[/tex]
[tex]6\cdot x -2\cdot a -4\cdot x +4\cdot a = 3\cdot x +3\cdot a[/tex]
[tex]6\cdot x -4\cdot x -3\cdot x = 3\cdot a -4\cdot a +2\cdot a[/tex]
[tex]-x = a[/tex]
[tex]x = -a[/tex]
d) [tex]\frac{2\cdot x}{5} - \frac{x-2\cdot a}{3} = \frac{a}{2}[/tex]
[tex]\frac{6\cdot x-5\cdot (x-2\cdot a)}{15} = \frac{a}{2}[/tex]
[tex]\frac{6\cdot x - 5\cdot x+10\cdot a}{15} = \frac{a}{2}[/tex]
[tex]2\cdot (x+10\cdot a) = 15 \cdot a[/tex]
[tex]2\cdot x = 5\cdot a[/tex]
[tex]x = \frac{5}{2}\cdot a[/tex]
2) a) [tex]\frac{3}{x} + \frac{5}{x+2} = 0[/tex]
[tex]\frac{3\cdot (x+2)+5\cdot x}{x\cdot (x+2)} = 0[/tex]
[tex]3\cdot (x+2) + 5\cdot x = 0[/tex]
[tex]3\cdot x +6 +5\cdot x = 0[/tex]
[tex]8\cdot x = - 6[/tex]
[tex]x = -\frac{3}{4}[/tex]
b) [tex]\frac{7}{x-2} = \frac{5}{x}[/tex]
[tex]7\cdot x = 5\cdot (x-2)[/tex]
[tex]7\cdot x = 5\cdot x -10[/tex]
[tex]2\cdot x = -10[/tex]
[tex]x = -5[/tex]
c) [tex]\frac{2}{x-3}-\frac{4\cdot x}{x^{2}-9} = \frac{7}{x+3}[/tex]
[tex]\frac{2}{x-3} - \frac{4\cdot x}{(x+3)\cdot (x-3)} = \frac{7}{x+3}[/tex]
[tex]\frac{1}{x-3}\cdot \left(2-\frac{4\cdot x}{x+3} \right) = \frac{7}{x+3}[/tex]
[tex]\frac{x+3}{x-3}\cdot \left[\frac{2\cdot (x+3)-4\cdot x}{x+3} \right] = 7[/tex]
[tex]\frac{2\cdot (x+3)-4\cdot x}{x-3} = 7[/tex]
[tex]2\cdot (x+3) -4\cdot x = 7\cdot (x-3)[/tex]
[tex]2\cdot x + 6 - 4\cdot x = 7\cdot x -21[/tex]
[tex]2\cdot x - 4\cdot x -7\cdot x = -21-6[/tex]
[tex]-9\cdot x = -27[/tex]
[tex]x = 3[/tex]
For this year's fundraiser, students at a certain school who sell at least 75 magazine subscriptions win a prize. If the fourth grade students at this school sell an average (arithmetic mean) of 47 subscriptions per student, the sales are normally distributed, and have a standard deviation of 14, then approximately what percent of the fourth grade students receive a prize
Answer:
The percentage is k = 2.3%
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 47[/tex]
The standard deviation is [tex]\sigma = 14[/tex]
Given that the sales are normally distributed and that students at a certain school who sell at least 75 magazine subscriptions win a prize then the percent of the fourth grade students receive a prize is mathematically represented as
[tex]P(X > 75) = P(\frac{X - \mu }{\sigma } > \frac{75 - \mu }{\sigma })[/tex]
Generally
[tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of \ X )[/tex]
So
[tex]P(X > 75) = P(Z > \frac{75 - 47 }{14 })[/tex]
[tex]P(X > 75) = P(Z > 2)[/tex]
From the standardized normal distribution table
[tex]P(Z > 2) =0.023[/tex]
=> [tex]P(X > 75) = 0.023[/tex]
The percentage of the fourth grade students receive a prize is
k = 0.023 * 100
k = 2.3%
The curve y=2x^3+ax^2+bx-30 has a stationary point when x=3. The curve passes through the point (4,2).
(A) Find the value of a and the value of b.
#secondderivative #stationarypoints
A stationary point at x = 3 means the derivative dy/dx = 0 at that point. Differentiating, we have
dy/dx = 6x ² + 2ax + b
and so when x = 3,
0 = 54 + 6a + b
or
6a + b = -54 … … … [eq1]
The curve passes through the point (4, 2), which is to say y = 2 when x = 4. So we also have
2 = 128 + 16a + 4b - 30
or
16a + 4b = -96
4a + b = -24 … … … [eq2]
Eliminate b by subtracting [eq2] from [eq1] and solve for a, then for b :
(6a + b) - (4a + b) = -54 - (-24)
2a = -30
a = -15 ===> b = 96
The square root of 3/100 is between what two numbers
9514 1404 393
Answer:
0.17 and 0.18
Step-by-step explanation:
Usually, a question like this asks for two integer values that bound the root. Here, those would be 0 and 1.
√(3/100) = (√3)/10 ≈ 0.17320508...
You can truncate this at any point to find a number lower than √.03, then add 1 to that value's least-significant digit to find a number higher than √.03.
For example, if we use 4 digits, the two numbers bounding the root could be ...
0.1732 and 0.1733
HELP PLEASE PLEASE :(
Answer:
16
Step-by-step explanation:
It’s a ratio.
x/12=21/28
21x=12*28
21x=336
x=336/21
x=16
What is the solution (x, y) to this system of linear equations? 2x – 3y = –6 x + 2y = 11
Answer:
x = 3, y = 4
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Consider the following information. 1 hour = 3.6 · 10^3 seconds 1 day = 24 hours 1 year = 3.65 · 10^2 days Use scientific notation to calculate the number of seconds in 3 days.
Answer:
2.592 x 10^5
Step-by-step explanation:
1st step: Calculate for 1 day.
if 1 hour = 3.6 X 10³
24 hrs = (3.6 x 10³) X (2.4 x 10¹)
= 3.6 x 2.4 X 10⁴
= 8.64 x 10⁴
2nd Step: Calculate for 3 days;
if 1 day = 8.64 x 10⁴
3 days = (8.64 x 10⁴) X (0.3 x 10¹)
= 8.64 x 0.3 x 10^5
= 2.592 x 10^5
What is $121 divided into ratio of 7:4
Answer:
77:44
Step-by-step explanation:
Since 7:4 is equal to 11 and 121/11, each ratio can be multiplied by 11.
Let s1 = k and define sn+1 = √4sn − 1 for n ≥ 1. Determine for what values of k the sequence (sn) will be monotone increasing and for what values of k it will be monotone decreasing.
Answer:
The answer is "[tex]\bold{\frac{1}{4}<k\leq 2+\sqrt{3}}[/tex]"
Step-by-step explanation:
Given:
[tex]\ S_1 = k \\\\ S_{n+1} = \sqrt{4S_n -1}[/tex] [tex]_{where} \ \ n \geq 1[/tex]
In the above-given value, [tex]S_n[/tex] is required for the monotone decreasing so, [tex]S_2 :[/tex]
[tex]\to \sqrt{4k-1} \leq \ k=S_1\\\\[/tex]
square the above value:
[tex]\to k^2-4k+1 \leq 0\\\\\to k \leq 2+\sqrt{3} \ \ \ \ \ and \ \ 4k+1 >0\\\\[/tex]
[tex]\bold{\boxed{\frac{1}{4}<k\leq 2+\sqrt{3}}}[/tex]
what is the end point of a ray
Answer:
point A is the rays endpoint
Step-by-step explanation:
Answer:
The "endpoint" of a ray is the origin point of the ray, or the point at which the ray starts.
Step-by-step explanation:
A ray starts at a given point, the endpoint, and then goes in a certain direction forever ad infinitum. The origin point of a ray is called "the endpoint".
Cheers.
HHHHHHHheeellllllppppp MEMEMEMEMMEMEMEMEMEEEEEEEE PLLLZZZZ
Another trader would like to carry out a hypothesis test about stocks that offer dividends. Why is this hypothesis test right-tailed? Select the correct answer below: This is a right-tailed test because a direction is not specified. This is a right-tailed test because a direction is specified. The population parameter is greater than the specified value. This is a right-tailed test because a direction is specified. The population parameter is less than the specified value. More information is needed.
Answer:
This is a right-tailed test because a direction is specified. The population parameter is greater than the specified value.
Step-by-step explanation:
The hypothesis testing technique is used to test an assumption regarding population parameter. Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. A right tailed test is where the most of data is in the right side. This is one tailed test where the direction is specified.
A Prefeitura da Cidade Feliz doou um
terreno para a Comunidade Viver Bem
discutir projetos que deveriam ser
implantados no local. Após um planejamento
participativo, ficou acertado que 45% da área
total desse terreno serão destinados a uma
creche;
3%,
para banheiros públicos e 12%
para uma academia de ginástica comunitária.
A sobra da área, que é de 960m² será
utilizada para uma pequena praça com
parque de lazer. Qual é a área total ocupada
pela creche, banheiros públicos e academia
de ginástica comunitária?
Aqui temos a seguinte divisao de terreno:
creche + banheiros + academia = 45% + 3% + 12% = 60%
O que sobra: Fazendo a conta, 100 - 60 = 40, restará 40%
No enunciado informa que sobraram 960m².
Logo concluimos que 40% = 960m²
Sendo assim, regra de 3:
m² %
960 -------- 40
X -------- 60
40X = 960 . 60
X = 57600/40
X = 1440
Logo 1440m² é destinado para: creche, banheiros públicos e academia
de ginástica comunitária.
O terreno tem um total de 1440 + 960 = 2400m²
para cada espaço - novamente diversas regra de 3:
→ creche = 45%
m² %
2400 -------- 100
X -------- 45
X = 108000/100 = 1080
→ banheiros públicos = 3%
m² %
2400 -------- 100
X -------- 3
X = 7200/100 = 72
→ academia de ginástica comunitária = 12%
m² %
2400 -------- 100
X -------- 12
X = 28800/100 = 288
provando:
60% = 1440m² (visto acima)
creche - 1080
banheiros - 72
academia - 288
1080 + 72 + 288 = 1440 (60%)
How many adults must be randomly selected to estimate the mean FICO (credit rating) score of working adults in a country? We want % confidence that the sample mean is within points of the population mean, and the population standard deviation is .
Answer: hello below is the complete question
How many adults must be randomly selected to estimate the mean FICO (credit rating) score of working adults in a country? We want 90% confidence that the sample mean is within 4 points of the population mean, and the population standard deviation is 66. Round up to the nearest whole number
answer : 737 adults
Step-by-step explanation:
confidence interval = 90% = 0.9
( E ) = 4
standard deviation = 66
first we have to calculate the value of a
a = 1 - confidence interval
= 1 - 0.9 = 0.10 hence a / 2 = 0.05
next find the value of Z a/2 from table
Z[tex]_{0.05}[/tex] = 1.645
The number of Adults selected can be determined using this relation
N = [tex](Z_{a/2} * (s/E))^2[/tex]
= [tex](Z_{0.05} * ( 66/4))^2[/tex]
= 737
A study was conducted to determine whether magnets were effective in treating pain. The values represent measurements of pain using the visual analog scale. Assume that both samples are independent simple random samples from populations having normal distributions. Use a significance level to test the claim that those given a sham treatment have pain reductions that vary more than the pain reductions for those treated with magnets.
n xbar s
Sham 20 0.41 1.26
Magnet 20 0.46 0.93
Answer and Step-by-step explanation: The null and alternative hypothesis for this test are:
[tex]H_{0}: s_{1}^{2} = s_{2}^{2}[/tex]
[tex]H_{a}: s_{1}^{2} > s_{2}^{2}[/tex]
To test it, use F-test statistics and compare variances of each treatment.
Calculate F-value:
[tex]F=\frac{s^{2}_{1}}{s^{2}_{2}}[/tex]
[tex]F=\frac{1.26^{2}}{0.93^{2}}[/tex]
[tex]F=\frac{1.5876}{0.8649}[/tex]
F = 1.8356
The critical value of F is given by a F-distribution table with:
degree of freedom (row): 20 - 1 = 19
degree of freedom (column): 20 - 1 = 19
And a significance level: α = 0.05
[tex]F_{critical}[/tex] = 2.2341
Comparing both values of F:
1.856 < 2.2341
i.e. F-value calculated is less than F-value of the table.
Therefore, failed to reject [tex]H_{0}[/tex], meaning there is no sufficient data to support the claim that sham treatment have pain reductions which vary more than for those using magnets treatment.