A number = x
Is multiplied by 6 = 6x
And the product is added to 4 = 6x + 4
The sum is equal to the product of 2 and 17 ; 6x + 4 = 2 * 17
Solve for x
6x + 4 = 2 * 17
Combine like terms
6x = 34 - 4
6x = 30
Divide both sides by 6
6x/6 = 30/6
x = 5
Answer:
5, hope this helped my love have a good rest of your day ^^
Step-by-step explanation:
the product of 2 and 17 is 34
34 - 4 is 30
30 devided by 6 is 5
therefore, by working backwords we can figure out that this math riddle would be equal to 5 ^^
A diver ascended 9/10 of a meter in 1/10 of a minute. What was the diver's rate of ascent?Show your work.
According to the given data we have the following:
A diver ascended 9/10 of a meter in 1/10 of a minute, hence a full minute=10/10 becuase 9/10*1/10=10/10
Therefore, in order to calculate the diver's rate of ascent we would make the following calculation:
diver's rate of ascent=9/10*10
diver's rate of ascent=9
Therefore, the rate would be 9 meters per minute
Find the angle of elevation from the base of one tower to the top of the second
This system can be represented by a triangle with base 350 m length and height 100 m length
The angle of elevation is given by:
[tex]\tan ^{-1}(\frac{100}{350})=\tan ^{-1}(\frac{2}{7})\approx0.28\text{ rad }\approx\text{ 16\degree}[/tex]Heads= 24Tails= 21Based on the table, what is the experimental probability that the coin lands on heads? Express your answer as a fraction
ok
Total number of results = 24 + 21
= 45
Probability that the coins lands on heads = 24/45
= 8/15
Result = 8/15
14. To surf the internet at the Airport costs $20,40 for 20 minutes and it costs $26.25 for 35minutes. How much would it cost to surf the internet for exactly 55 minutes.
Cost = $20.40 / 20 min
Cost = $26.25 / 35 min
To calculate the cost to suft 55 min just add the previous values given
Cost = 20.40 + 26.25
= $46.65
Points A, B, and C are collinear and point B lies in between points A and C. If AB = 3x + 1, BC = 15, and AC = 7x + 1, find AC. Show work please
Answer:
AC = AB + BC + AC
AC= 3×+1+15+7×+1
AC= 3x+7×+1+15+1
AC=10×+17
A survey of visitor at national park was conducted to determined the preferred activity. The survey results are shown in the table. Based on this information which prediction about the preferred activity for the next 200 visitors to the park is the most reasonable.
Given:
A survey of visitors at a national park is shown in the table.
a) The number of visitors who preferred champing is 28.
The number of visitors who preferred hiking tails is 22.
And The number of visitors who preferred champing is 6 more than visitors who preferred hiking tails.
Option a) is incorrect.
b) Hiking trails - water sports= 22-14=8
c) Water sports - biking trails = 14-16= -2
Option c) is incorrect.
d)
[tex]\begin{gathered} \text{Camping}=2\times water\text{ sports} \\ =2\times14 \\ =28 \end{gathered}[/tex]From the given options b) and d) shows the correct predictions.
Amoung these two options most reasonable is option d) for next 200 visitors.
Use the sample data and confidence level given below to complete parts (a) through (d)A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n = 1047 and x = 545 whosaid "yes." Use a 95% confidence level.A. find the best point of estimate of the population of portion p.B. Identify the value of the margin of error E. (E= round to four decimal places as needed.)C. Construct the confidence interval. (
a. The best point of estimate of the population of portion p is given by the formula:
[tex]p^{\prime}=\frac{x}{n}[/tex]where x is the number of successes x=545 and n is the sample n=1047.
Replace these values in the formula and find p:
[tex]p^{\prime}=\frac{545}{1047}=0.521[/tex]b. The value of the margin of error E is given by the following formula:
[tex]E=(z_{\alpha/2})\cdot(\sqrt[]{\frac{p^{\prime}q^{\prime}}{n}})[/tex]Where z is the z-score at the alfa divided by 2, q'=1-p'.
As the confidence level is 95%=0.95, then alfa is 1-0.95=0.05, and alfa/2=0.025
The z-score at 0.025 is 1.96.
Replace the known values in the formula and solve for E:
[tex]\begin{gathered} E=1.96\cdot\sqrt[]{\frac{0.521\cdot(1-0.521)}{1047}} \\ E=1.96\cdot\sqrt[]{\frac{0.521\cdot0.479}{1047}} \\ E=1.96\cdot\sqrt[]{\frac{0.2496}{1047}} \\ E=1.96\cdot\sqrt[]{0.0002} \\ E=1.96\cdot0.0154 \\ E=0.0303 \end{gathered}[/tex]c. The confidence interval is then:
[tex]\begin{gathered} (p^{\prime}-E,p^{\prime}+E)=(0.521-0.0303,0.521+0.0303) \\ \text{Confidence interval=}(0.490,0.551) \end{gathered}[/tex]d. We estimate with a 95% confidence that between 49% and 55.1% of the people felt vulnerable to identity theft.
Rewrite the equation in standard form. Y+3=-(x-5)
To rewrite the given equation (point slope) into standard form:
1. Remove parentheses: Multiply each term in the parentheses by -1:
[tex]\begin{gathered} y+3=(-1)(x)+(-1)(-5) \\ \\ y+3=-x+5 \end{gathered}[/tex]2. Add x in both sides of the equation:
[tex]\begin{gathered} x+y+3=-x+x+5 \\ x+y+3=5 \end{gathered}[/tex]3. Subtract 3 in both sides of the equation:
[tex]\begin{gathered} x+y+3-3=5-3 \\ x+y=2 \end{gathered}[/tex]Then, the given equation in standard form is: x+y=2Which method of finding probabilities do you prefer: lists, binompdf, binomcdf, nCr, etc.? Why?
For BinomPDF and BinomCDF we have a distribution that gives you the probability to have some number of successes, the difference is that PDF gives you only one specific number of successes, and the CDF gives you a range of successes probabilities.
Lists are the basic form to find a probability, you have to write all the cases and count the different groups of them, then divide by the total of cases.
NCR and NPR are the classic counting method to reach the number of combinations or permutations that a situation could have, is very useful and very quick to calculate the interest data or the number of combinations that may have a group of cases.
A ball is thrown from an initial height of 3 meters with an initial upward velocity of 30 m/s. The ball’s height h (in meters) after t seconds is given by the following. h=3+30t-5t^2 Find all values of t for which the ball’s height is 13 meters. Round your answer(s) to the nearest hundredth.
Answer:
The values of t for which the ball's height is 13 meters is;
[tex]\begin{gathered} t=0.35\text{ s} \\ or \\ t=5.65\text{ s} \end{gathered}[/tex]Explanation:
The function of the ball's height h (in meters) is given as;
[tex]h=3+30t-5t^2[/tex]the value of time t for which the ball's height is 13 meters, can be derived by substituting h=13 into the function of h.
[tex]\begin{gathered} h=3+30t-5t^2 \\ 13=3+30t-5t^2 \\ 3+30t-5t^2=13 \end{gathered}[/tex]subtract 13 from both sides and solve the quadratic equation;
[tex]\begin{gathered} 3+30t-5t^2-13=13-13 \\ -5t^2+30t-10=0 \end{gathered}[/tex]solving the quadratic equation, using the quadratic formula;
[tex]\begin{gathered} t=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ t=\frac{-30\pm\sqrt{30^2-4\times-5\times-10}}{2\times-5} \\ t=\frac{-30\pm\sqrt{900-200}}{-10} \\ t=\frac{-30\pm\sqrt{700}}{-10} \\ t=0.3542=0.35 \\ or \\ t=5.64575=5.65 \end{gathered}[/tex]The values of t for which the ball's height is 13 meters is;
[tex]\begin{gathered} t=0.35\text{ s} \\ or \\ t=5.65\text{ s} \end{gathered}[/tex]A person who wants to get in shape goes to a local gym that advertises 31 training sessions for $1908. Find the cost of 133 training sessions. Round your answer to the nearest cent.
According to the given data we have the following:
31 training sessions=$1908
In order to calculate the cost of 133 training sessions we would have to apply the 3 rule.
So, if 31 training sessions__________________$1908
133 training sessions______________________x
Therefore, x=(133 training sessions*$1908)/31 training sessions
x=$253,764/31 training sessions
x=$8,186
The cost of 133 training sessions would be $8,186
If 9:x=x:4, then x = 3618246
Answer
Option D is correct.
x = 6
Explanation
9 : x = x : 4
To solve this, we know that ratios can be written in fraction form
(9/x) = (x/4)
[tex]\begin{gathered} \frac{9}{x}=\frac{x}{4} \\ \text{Cross multiply} \\ x^2=9\times4 \\ x^2=36 \end{gathered}[/tex]Take the square root of both sides
√(x²) = √(36)
x = 6
Hope this Helps!!!
cam you show me the conversion from mm to cm to m to dm to km please
To determine the conversion from mm to cm to m to dm to km:
[tex]\begin{gathered} \operatorname{mm}\text{ => Millimtere} \\ \operatorname{cm}=>\text{centimetre} \\ m\Rightarrow\text{ metre} \\ dm\Rightarrow\text{ decimetre} \\ \operatorname{km}-\text{kilometre} \end{gathered}[/tex]Conversion from mm to cm =
[tex]10\text{ mm }\Rightarrow\text{ 1 cm}[/tex]Conversion from cm to m
[tex]100\operatorname{cm}\Rightarrow\text{ 1m}[/tex]Conversion from m to dm
[tex]1m\Rightarrow\text{ 10dm}[/tex]Conversion from dm to km
[tex]10000dm\Rightarrow\text{ }1\text{ km}[/tex]Hence the correct conversion are
10 mm = 1 cm
100 mm = 1 dm
1000 mm = 1 mm
1000000 mm = 1 km
Madelyn incorrectly followed the set of directions when she transformed pentagon PENTA.The directions are listed below the coordinate plane. What was the error Madelyn made?A. She rotated, but not 180°B. She reflected over the x-axis instead of the y-axisC. She translated 4 units to the left instead of the rightD. She did not make a mistake
Solution:
Given the transformation below:
Given the directions:
[tex]\begin{gathered} Rotate\text{ 180 degrees} \\ Reflect\text{ over the y-axis} \\ Translate\text{ 4 unnts to the right} \end{gathered}[/tex]Step 1: Give the coordinates of the vertices of pentagon PENTA.
Thus,
[tex]\begin{gathered} P(-5,5) \\ E(-3,\text{ 5\rparen} \\ N(-4,\text{ 4\rparen} \\ T(-3,\text{ 2\rparen} \\ A(-5,\text{ 2\rparen} \end{gathered}[/tex]step 2: Rotate the pentagon 180 degrees.
For 180 degrees rotation, we have
[tex]\begin{gathered} A(x,y)\to A^{\prime}(-x,\text{ -y\rparen} \\ where \\ A^{\prime}\text{ is an image of A} \end{gathered}[/tex]Thus, the coordinates of pentagon becomes
[tex]\begin{gathered} P(5,\text{ -5\rparen} \\ E(3,\text{ -5\rparen} \\ N(4,\text{ -4\rparen} \\ T(3,\text{ -2\rparen} \\ A(5,\text{ -2\rparen} \end{gathered}[/tex]The image is shown below:
step 3: Reflect over the y-axis.
For reflection over the y-axis, we have
[tex](x,y)\to(-x,y)[/tex]This, we have the image to be
step 4: Translate 4 units to the right.
For translation by 4 units to the right, we have
[tex](x,y)\to(x+4,\text{ y\rparen}[/tex]This gives
Hence, the mistake Madelyn made was that she reflected over the x-axis instead of the y-axis.
The correct option is B.
5. Solve the system of equations by graphing. y = -x + 2 3x + 3y = 6
Answer:
The system of equations has infinite number of solutions.
The solution to the system of equations is any point on the line of the graph.
Explanation:
Given the system of equations;
[tex]\begin{gathered} y=-x+2 \\ 3x+3y=6 \end{gathered}[/tex]Plotting the two equations using a graph calculator we have;
From the graph, we can observe that the line of the two equations fall on each other.
That means that the equations are the same.
Therefore, the system of equations has infinite number of solutions.
The solution to the system of equations is any point on the line of the graph.
The perimeter of the triangle PQR is 94cm. What is the length of PQ?
the length of PQ is 33 cm
Explanation:The perimeter of the triangle = 94 cm
The triangle is an isosceles triangle as two of its sides are equal
From the diagram:
PQ = RQ
Perimeter of triangle = PQ + PR + RQ
PR = 28 cm
94 = PQ + 28 + RQ
94 = 2PQ + 28
94 - 28 = 2PQ
66 = 2PQ
divide both sides by 2:
66/2 = 2PQ/2
PQ = 33
Hence, the length of PQ is 33 cm
Find the derivative :f(x) = 6x⁴ -7x³ + 2x + √2
We need to find the derivative of the function
[tex]f\mleft(x\mright)=6x^{4}-7x^{3}+2x+\sqrt{2}[/tex]The derivative of a polynomial equals the sum of the derivatives of each of its terms.
And the derivative of each term axⁿ, where a is the constant multiplying the nth power of x, is given by:
[tex](ax^n)^{\prime}=n\cdot a\cdot x^{n-1}[/tex]Step 1
Find the derivatives of each term:
[tex]\begin{gathered} (6x^4)^{\prime}=4\cdot6\cdot x^{4-1}=24x^{3} \\ \\ (-7x^3)^{\prime}=3\cdot(-7)\cdot x^{3-1}=-21x^{2} \\ \\ (2x)^{\prime}=1\cdot2\cdot x^{1-1}=2x^0=2\cdot1=2 \\ \\ (\sqrt[]{2})^{\prime}=0,\text{ (since this term doesn't depend on x, its derivative is 0)} \end{gathered}[/tex]Step 2
Add the previous results to find the derivative of f(x):
[tex]f^{\prime}(x)=24x^{3}-21x^{2}+2[/tex]Answer
Therefore, the derivative of the given function is
[tex]24x^3-21x^2+2[/tex]Which of the following names the figure in the diagram below?
O A. Triangle
O B. Prism
O C. Polygon
O D. Pyramid
O E. Cylinder
O F. Cube
Step 1
A triangular prism is a 3D shape that looks like an elongated pyramid. It has two bases and three rectangular faces.
Step 2:
A triangular prism has two triangular bases and three rectangular sides and is a pentahedron because it has five faces. Camping tents, triangular roofs and "Toblerone" wrappers -- chocolate candy bars -- are examples of triangular prisms.
Final answer
B. Prism
10÷5+10-9×1110 / 5 + 10 - 9 * 11 equals what
Follow the order to solve polynomials
1. Powers and roots
2. Divisions and products
3. Sums and substractions
[tex]\begin{gathered} \frac{10}{5}+10-9\cdot11 \\ 2+10-99 \\ 12-99 \\ -87 \end{gathered}[/tex]The answer is -87
Which of the following equations represents the line that passes throught the points (2, -6) and(-4,3)?A.y= -3/2x - 7B.y= -2/3x - 3C.y= -2/3x + 1/3D.y= -3/2x - 3
Given two points (x1, y1) and (x2, y2), the slope (m) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing with points (2, -6) and (-4, 3), we get:
[tex]m\text{ = }\frac{3-(-6)}{-4-2}=\frac{9}{-6}=-\frac{3}{2}[/tex]slope-intercept form of a line:
y = mx + b
where m is the slope and b is the y-intercept.
Replacing with point (2, -6) and m = -3/2, we get:
-6 = -3/2(2) + b
-6 = -3 + b
-6 + 3 = b
-3 = b
Finally, the equation is:
y = -3/2x - 3
Match the following items.1. (-14) + 81 = 81 + (-14)commutative property of addition312424 +. 15associative property of addition2.(24 + 15)3313 173.= 117 134. -72 + 0 = -72distributive propertymultiplicative inverse5. 101 + (29 +417) = (101 +29) + 417additive identity
The Solution.
1.
[tex](-14)+81=81+(-14)\text{ }\Rightarrow Commutative\text{ property of addition}[/tex]2.
[tex]\frac{1}{3}(24+15)=\frac{1}{3}.24+\frac{1}{3}.15\text{ }\Rightarrow\text{ Distributive property}[/tex]3.
[tex]\frac{13}{17}\times\frac{17}{13}=1\text{ }\Rightarrow Multiplicative\text{ inverse}[/tex]4.
[tex]-72+0=-72\text{ }\Rightarrow\text{ }Additive\text{ Identity}[/tex]5.
what represents the factorization of the trinomial below?[tex] {x}^{2} - x - 20[/tex]
The expression given is,
[tex]x^2-x-20[/tex]Factorize the expression above
[tex]\begin{gathered} Break\text{ the expressions into two groups} \\ \left(x^2+4x\right)+\left(-5x-20\right) \\ Factorize\text{ out the common terms} \\ =x\left(x+4\right)-5\left(x+4\right) \\ \mathrm{Factor\:out\:common\:term\:}x+4 \\ =\left(x+4\right)\left(x-5\right) \end{gathered}[/tex]Hence, the answer is
[tex]\left(x+4\right)\left(x-5\right)[/tex]whats the length of RS,UW,UVwhat is the value of x and y
In the given triangle,
it is given that,
U is the midpoint of RS, V is the midpoint of ST and W is the midpoint of RT
so,
UR = US
VT = VS
WT = WR
put the values,
UR = US
12 = US
so, RS = 2 x UR = 2 x 12 = 24
VT = VS
11 = 2x
x = 11/2
x = 5.5
so, TS = 2 x 11 = 22
WT = WR
3y = 15.9
y = 15.9/3
y = 5.3
so, RT = 2 x 15.9 = 31.8
also, UV = 1/2 RT
UV = 1/2 x 31.8 = 15.9
UW = 1/2x TS
UW = 1/2 x 22 = 11
VW = 1/2 RS
VW = 1/2 x 24 = 12
A swim team consist of seven boys and four girls a relay team of four swimmers is chosen at random from the team members what is the probability that three boys are selected for the relay team given that the first selection was a girl express your answer as a fraction in lowest terms or a decimal rounded to the nearest million
At start, we have:
- 7 boys
- 4 girls
It is given that the first selection was a girl. Since there were 4 girls, there is 3 left to be picked. So we have:
- 1 girl picked
- 7 boys to be picked
- 3 girls to be picked
We want the next 3 pickes to be boys.
The probability that the first pick will be a boy is the number of boys to be picked from over the total team left to be picked from. We have 7 boys and a total of 7 + 3 = 10 members, so:
[tex]P_1=\frac{7}{10}[/tex]Next, we want another pick of boy, but now we have got only
- 6 boys
- 3 girls
So, the probability of the second pick to be boy is:
[tex]P_2=\frac{6}{9}[/tex]And for the third, we have:
- 5 boys
- 3 girls
Probability of
[tex]P_3=\frac{5}{8}[/tex]Since we want these three to occur, the final probability is the product of them:
[tex]P=P_1\cdot P_2\cdot P_3=\frac{7}{10}\cdot\frac{6}{9}\cdot\frac{5}{8}=\frac{7}{1}\cdot\frac{1}{3}\cdot\frac{1}{8}=\frac{7}{24}[/tex]So, the answer as a fraction in the lowest form is:
[tex]\frac{7}{24}[/tex]To raise money for charity, Bob and some friends are hiking across the continent of Asia. While out on the trail one day, one of his Jordian friends asks Bob for the temperature. He glances at his precision sports watch and sees that the temperature is -12.9 F. What is this temperature in degrees C Celsius ()?
ANSWER
[tex]-24.9[/tex]EXPLANATION
Given;
[tex]-12.9F[/tex]To convert to degree Celsius, we use the formula;
[tex]\begin{gathered} \frac{5}{9}(F-32) \\ \\ \end{gathered}[/tex]Substituting F;
[tex]\begin{gathered} \frac{5}{9}(-12.9-32) \\ =\frac{5}{9}\times-44.9 \\ =-\frac{224.5}{9} \\ =-24.94 \\ \cong-24.9 \end{gathered}[/tex]12. On Monday, a museum had 150 visitors. On
Tuesday, it had 260 visitors.
a. Choose Efficient Methods Estimate the
percent change in the number of visitors to
the museum.
b. About how many people would have to visit
the museum on Wednesday to have the same
percent change from Tuesday to Wednesday
as from Monday to Tuesday? Explain your
answer.
a. The percent change in the number of visitors to the museum is 73.33%
b. The people that would have to visit the museum on Wednesday to have the same
percent change is 450.
How to calculate the percentage?From the information given, on Monday, a museum had 150 visitors. On Tuesday, it had 260 visitors. It should be noted that the increase will be:
= 260 - 150
= 110
The percentage increase will be:
= Increase in value / Original value × 100
= 110/150 × 100
= 73.33%
The number of people that should visit in Wednesday will be:
= 260 + (73.33% × 260)
= 260 + 190
= 450
Learn more about percentages on:
brainly.com/question/24304697
#SPJ1
Hi, can you help me answer this question please, thank you
The confidence interval 219.9 ± 57.6 is just equal to:
219.9 - 57.6 = 162.3
219.9 + 57.6 = 277.5
The confidence interval 219.9 ± 57.6 can also be written as between 162.3 and 277.5. In trilinear inequality, it is:
[tex]162.3<\mu<277.5[/tex]9. (a) The diagram below, not drawn to scale, shows a circle, where two lines intersect at point C. The points A, B, D and I lie on the circumference of the circle Note that ABDE is a right-angled triangle and BD is the diameter of the circle. A 66° D 78° C E B Determine, giving a reason for your answer, (1) ВСЕ 121 (ii) BDE 121 (iii) DBE 121
(i)
The angle 78° is supplementary to the angle BCE. Then we have:
[tex]\begin{gathered} 78\degree+B\hat{C}E=180\degree \\ B\hat{C}E=180\degree-78\degree \\ B\hat{C}E=102\degree \end{gathered}[/tex](ii)
When the vertex of a angle formed by two segments is located on the circle, the corresponding arc formed by the two segments is the double of the angle. Then we have:
[tex]\begin{gathered} B\hat{A}E=B\hat{D}E=\frac{arc\text{ BR}}{2} \\ B\hat{A}E=66\degree \\ \therefore B\hat{D}E=66\degree \end{gathered}[/tex](iii)
Since BDE is a right triangle, we have:
[tex]\begin{gathered} D\hat{B}E+B\hat{D}E+90\degree=180\degree \\ D\hat{B}E+66\degree+90\degree=180\degree \\ D\hat{B}E=180\degree-90\degree-66\degree \\ D\hat{B}E=24\degree \end{gathered}[/tex]Look at the graph of f(x). Which of the following are true? Select all that apply. 2 answers
Answer:
Explanation:
Answer:
A. [tex]f(x)[/tex] is [tex]y=sec(x-\pi )[/tex] shifted 6 units up.
C. [tex]f(x)[/tex] is [tex]y=sec(x)+6[/tex] shifted [tex]\pi[/tex] units to the left.
Step-by-step explanation:
If you guessed the answer to this question, or did not answer, go back and review how to write to equation of a trigonometric function.
Your welcome...
Suppose y = 6x −5. Find y if:x = −1/6y = ?
To find y, you can follow the steps:
Step 1: Substitute x by -1/6 in the equation.
[tex]\begin{gathered} y=-6x-5 \\ y=6\cdot(-\frac{1}{6})-5 \end{gathered}[/tex]Step 2: Solve the equation.
[tex]\begin{gathered} y=-\frac{6}{6}-5 \\ y=-1-5 \\ y=-6 \end{gathered}[/tex]Answer : y = -6.