Since the variable we want to represent is distance, then the most meaningful letter would be
B. d
since it remind us that we are talking about distance.
A certain drug is made from only two ingredients: compound B. There are 4 millimeters of compound A used for every 3 milliliters of compound B. If a chemist wants to make 406 milliliters of the drug, how many milliliters of comped B are needed
Given:
4 milliliter of compounf A used for every 3 milliliter of compound B.
That mean ratio is:
[tex]4\colon3[/tex]ler "x" the multiplier then:
[tex]\begin{gathered} 4x=\text{ amount of compound A} \\ 3x=\text{ amount of compound B} \end{gathered}[/tex]If chemist wants to make 406 milliliter that mean:
[tex]\begin{gathered} 4x+3x=406 \\ 7x=406 \\ x=\frac{406}{7} \\ x=58 \end{gathered}[/tex]The compound B needed is:
"3x" then the value is:
[tex]\begin{gathered} =3x \\ =3(58) \\ =174 \end{gathered}[/tex]So 174 milliliter used of compound B
An investment is initially worth $10,000. Write a formula for the value of this investment for each situation described below.
Using the compound interest formula:
The value increases by 7% every year:
[tex]V(t)=10000(1+0.07)^t[/tex]The value increases by 7% every 3 years:
[tex]V(t)=10000(1+0.07)^{\frac{t}{3}}[/tex]The value increases by 7% every six months:
[tex]V(t)=10000(1+\frac{0.07}{2})^{2t}[/tex]Necesito ayuda en una tarea de matemáticas pero es muy difícil si me pueden ayudar se lo agradezco. Es muy larga lo que dice es the area of the triangle above will be equal one half of a rectangle that is 5 units long _ units wide.( input only while numbers, such as 8.)
step 1
Find out the area of the triangle
[tex]A=\frac{1}{2}*b*h[/tex]where
b=5 units
h=4 units
substitute
[tex]\begin{gathered} A=\frac{1}{2}*5*4 \\ A=10\text{ units}^2 \end{gathered}[/tex]step 2
The formula to calculate the area of a rectangle is given by
[tex]A=L*W[/tex]where
Remember that the area of the triangle is on half of the rectangle
area of the triangle is 10 square units
that means
The area of the rectangle is 20 square units
so
we have
A=20 unit2
L=5 units
W=?
substitute in the formula
20=(5)*(W)
solve for w
w=20/5
w=4 unitsuse the quadratic model y= -4x^2 + 8x + 8
Hello!
First of all, let's rewrite the quadratic equation:
[tex]y=-4x^2+8x+8[/tex]To solve it, let's replace where we have x by 100, look:
[tex]\begin{gathered} y=-4\cdot(100)^2+8\cdot(100)+8 \\ y=-4\cdot10,000+800+8 \\ y=-40,000+808 \\ \boxed{y=-39,192} \end{gathered}[/tex]Answer:y= -39,192
Can you explain my work
For both figures, we need to count the number of squares and possible triangles in them.
Figure A:
In figure A, we have 9 squares and one triangle. The area of a triangle is:
[tex]A=\frac{base\cdot Altitude}{2}=\frac{1\cdot3}{2}=\frac{3}{2}=1.5[/tex]So, the area of figure A is 9 squares + 1.5 squares = 10.5 squares units.
Figure B:
We have 14 squares. We also have 4 small triangles that are equivalent to 2 squares. The final area is the triangle (applying the same formula than before):
[tex]A=\frac{b\cdot Altitude}{2}=\frac{1\cdot5}{2}=\frac{5}{2}=2.5[/tex]Then, we have, for figure B: 14 squares + 2 squares + 2.5 squares = 18.5 square units.
Therefore, Figure A is 10.5 square units, and Figure B is 18.5 square units.
Three people are sitting on a bus. Morgan is seated 24 feet directly behind Jibril and 7 feet directly left of Teyla. Jibril is __ feet from Teyla.
Answer:
Jibril is 25 feet from Teyla.
Step by step explanation:
Then we solve it by the Pythagorean theorem.
[tex]c^2=a^2+b^2[/tex]a= 24
b= 7
c= x
[tex]x^2=24^2+7^2[/tex][tex]x\text{ =}\sqrt[]{24^2+7^2}\text{ = }\sqrt[]{625}\text{ =25}[/tex]Hello , just need an explanation with my son’s hw .
We have the next fractions so we will simplify them
[tex]\frac{86}{100}=\frac{\frac{86}{2}}{\frac{100}{2}}=\frac{43}{50}[/tex][tex]\frac{90}{100}=\frac{9}{10}[/tex][tex]\frac{94}{100}=\frac{47}{50}[/tex][tex]\frac{101}{100}[/tex]As we can see the point is represented by
[tex]\frac{94}{100}[/tex]
find the sum.1 1/4 + 5/6
Okay, here we have this:
Considering the provided sum, we are going to perform it, so we obtain the following:
[tex]\begin{gathered} 1\frac{1}{4}+\frac{5}{6} \\ \\ =\frac{5}{4}+\frac{5}{6} \\ \\ =\frac{30+20}{24} \\ \\ =\frac{50}{24} \\ \\ =\frac{25}{12} \end{gathered}[/tex]Finally we obtain that the result of the sum is 25/12.
what is the value of the expression 3.0 x 10 to the power of 6 then 1.5 x 10 to the power of 4 the answers are 2.0 x 10 to the power of 2 2.0 x 10 to the power of 1 1.5 x 10 to the power of 2 1.5 x 10 to the power of 10
We have to evaluate "3.0 x 10 to the power of 6 divided by 1.5 x 10 to the power of 4"
Then we have:
[tex]\frac{3.0\cdot10^6}{1.5\cdot10^4}=\frac{3.0}{1.5}\cdot10^{(6-4)}=2.0\cdot10^2[/tex]The answer is 2.0 * 10^2.
Find the coordinates of each point under the given rotation about the origin (5, -5); 90 clockwise
Step 1. The point we have is:
[tex](5,-5)[/tex]We will label this point as (x, y):
[tex]\begin{gathered} (x,y)\to(5,-5) \\ x=5 \\ y=-5 \end{gathered}[/tex]Step 2. We need to make a rotation of this point about the origin,
The rule for a rotation of 90° about the origin clockwise is:
[tex]\boxed{(x,y)\longrightarrow(y,-x)}[/tex]Step 3. Applying the transformation from step 2 to the point from step 1:
[tex]\begin{gathered} \boxed{(x,y)\longrightarrow(y,-x)} \\ \boxed{(5,-5)\longrightarrow(-5,-5)} \end{gathered}[/tex]We put the old y-value in the place of the new x-value, and we put the old x-value in the place of the new y-value with the opposite sign.
(-5,-5) is the result.
Answer:
(-5, -5)
Simplify the rational expression. You may want to refer to Example 12 of this8x - 9/9 - 8x
ANSWER
[tex]-1[/tex]EXPLANATION
We want to simplify the rational expression given:
[tex]\frac{8x-9}{9-8x}[/tex]To do this, rewrite the denominator and simplify:
[tex]a-b=-(b-a)[/tex]This implies that:
[tex]\begin{gathered} \frac{8x-9}{-(8x-9)} \\ \Rightarrow\frac{1}{-1} \\ \Rightarrow-1 \end{gathered}[/tex]That is the answer.
Express each function as a function of an acute angleA) tan 226B) sin(-46.6)
Explanation
Part 1: tan 226
Angle 226 lies in the third quadrant. This can be seen below.
In the above, the principal angle is 226, therefore, the acute angle becomes,
[tex]226-180=46[/tex]Since tan is positive in the third quadrant, therefore
Answer: tan 46
Part B: Sin-46.6
In trigonomtery,
[tex]sin(-a)=-sina[/tex]Therefore;
[tex]sin(-46.6)=-sin46.6[/tex]Answer: -sin 46.6
The product of 2x-3 and x+4 can be expressed asA) 2x^2+5x-12B) 3x+1C) 2x^2+x-12D) 2x^2-12
The given product is
[tex](2x-3)(x+4)[/tex]We have to use the distributive property
[tex]2x\cdot x+2x\cdot4-3\cdot x-3\cdot4=2x^2+8x-3x-12[/tex]Then, we reduce like terms
[tex]2x^2+5x-12[/tex]Hence, the answer is A.I put a photo. 4 and 2 are the sides
The area of a triangle is given by the formula
[tex]A=\frac{1}{2}bh[/tex]Where
b is the length of the base
h is the height of he triangle
Looking at the figure, we can see:
[tex]\begin{gathered} b=4 \\ h=2 \end{gathered}[/tex]Substituting this information into the formula, we have:
[tex]\begin{gathered} A=\frac{1}{2}bh \\ A=\frac{1}{2}(4)(2) \\ A=4 \end{gathered}[/tex]AnswerArea = 4 sq. units.
The y-intercept of this regression line is 11. What does this tell you about the relationship between the amount of fertilizer and the height of the seedlings?
The y intercept in a regression line is the point where the line of best fit meets the y axis. It is the expected mean value of y when x=0.
In the given graph, x cooridnate represents the amount of fertilisers and the y coordinate represents the height of the seedlings.
Therefore, the y intercept tells the mean value of the height of a seedling when no fertiliser is used. Hence, we cay say that the mean value of the height of a seedling when no fertiliser is used is 11 cm.
it has no reflectional symmebry it has no rotational symmetry it has reflectional symmetry with six lines of symmetry it has rotational symmetry with an angle of rotation of 30°
Lets draw a picture:
Then, we can see that our figure has a rotational symmetry with an angle of rotation of 30 degrees because if we rotate the figure 30 degrees the figure coincides with itself.
Using the figure, calculate the total surface area of the pyramid.
Given:
There is a figure given in the question
Required:
We need to find the surface area of given figure of pyramid
Explanation:
First we need to find the side of base square
use tan function
[tex]\begin{gathered} \tan30=\frac{SM}{DM} \\ \\ \frac{1}{\sqrt{3}}=\frac{6}{DM} \\ \\ DM=6\sqrt{3} \end{gathered}[/tex]now to find the side of base square is
[tex]DC=2DM=12\sqrt{3}[/tex]The surface area of pyramid is
[tex]TSA=\frac{1}{2}Pl+B[/tex]where P is base of perimeter
l is the slant height which is 6 cm
B is the base area
now find P
[tex]P=4*12\sqrt{3}=48\sqrt{3}\text{ cm}[/tex]now find B
[tex]B=12\sqrt{3}*12\sqrt{3}=432\text{ cm}^2[/tex]now substitute all the values in the formula of Total surface area of pyramid
[tex]TSA=\frac{1}{2}Pl+B=\frac{1}{2}*48\sqrt{3}*6+432[/tex]simplify as:
[tex]\begin{gathered} =249.4+432 \\ =681.4\text{ cm}^2 \end{gathered}[/tex]Final answer:
Total surface area of given figure is 681.4 square cm
Im an older lady and im not the best at word problems please explain
EXPLANATION
We can see in the Venn diagram the following facts:
As the number of students that just visited Spain is 5 because the statement says that 16 visited to Spain and we have in the Venn Diagram 5+4+2+?=16 visitors of Spain, the unknown value is equal to 5.
As the total number of students is equal to 37 and the number of students that have visited some of the three countries is equal to the sum of all the given numbers:
9+ 5 + 4 + 4 + 5 + 2 + 5 = 34 students
In conclusion, the number of students that have not been to Germany, Spain or France is 3
The point P = (x, — 5/7) lies on the unit circle shown below. What is the value of xin simplest form?
The point (x,y) on unit circle is
[tex](x,y)=(\cos \theta,\sin \theta)[/tex]We know y is "sin theta" and sin is "opposite" over "hypotenuse". Thus, we can draw a triangle
We see that "5" is opposite of theta and 7 is the hypotenuse.
To get x, we use the pythagorean theorem:
[tex]\begin{gathered} \text{leg}^2+\text{AnotherLeg}^2=\text{Hypotenuse}^2 \\ x^2+5^2=7^2^{} \\ x^2+25=49 \\ x^2=49-25 \\ x^2=24 \\ x=\sqrt[]{24} \\ x=2\sqrt[]{6} \end{gathered}[/tex]From unit circle formula, we know value of x is cos. Thus, we take the cosine ratio, adjacent over hypotenuse.
Adjacent is 2 Sqrt(6) and Hypotenuse is 7 Thus,
[tex]x=\frac{2\sqrt[]{6}}{7}[/tex]
jada's pet turtle walked 10 ft and then half that length again. What is the total distance walked by the turtle?
half of 10 ft is 10/2 = 5ft
total distance = 10 ft + 5 ft = 15 ft
below are the angle measurements inside when it's of a trapezoid cell in a table with the correct side lengths and angle measurement the figure was Delight
we know that
The dilation is a no-rigid transformation that produce similar figures
That means, that the correspondind sides are proportional and the corresponding angles are congruent
The length side of the image is equal to the scale factor multiplied by the length of the preimage
the scale factor is 4 (given)
so
Side B=17 in ---------> image side B'=17(4)=68 in
Side C =18 in ---------> Side C'=18(4)=72 in
Side D=23 in -----------> Side D'=23(4)=92 in
the angles are congruent
Angle B=55 degrees -----------> Angle B'=55 degrees
Angle C=120 degrees ---------> Angle C'=120 degrees
Angle D=140 degrees -------> Angle D'=140 degrees
1,000 raffle tickets were sold. There will be one first prize of $1,000 and one second prize of $500. The rest of the tickets will win nothing. Use the chart to calculate the expected value.
The value of the Variance is $1,247.75 and the value of Standard Deviation is $35.32.
What is meant by standard deviation ?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
The standard deviation reveals the degree of data skewedness. It gauges how far away from the mean each observed value is. Approximately 95% of values in any distribution will be within two standard deviations of the mean.
Karl Pearson is credited with giving SD the name "standard deviation." I wouldn't guess anything more than that he wanted to suggest it as a benchmark. If anything, standardization references either stand alone or make an indirect reference to SD.
Therefore the value of variance is $1,247.75 and the value of Standard Deviation is $35.32.
The complete question is :1,000 raffle tickets were sold. There will be one first prize of $1,000 and one second prize of $500. The rest of the tickets will win nothing. Use the following table to calculate the variance and standard deviation. μ = $1.50.
To learn more about standard deviation refer to:
https://brainly.com/question/475676
#SPJ1
Let O be an angle in quadrant II such that csc =4"Find the exact values of tan 0 and cos 0.
The tangent function is given by:
[tex]\tan (\theta)=\frac{opposite}{adjacent}=-\frac{4}{\sqrt[]{65}}[/tex]And the cosine function is:
[tex]\cos (\theta)=\frac{adjacent}{hypotenuse}=-\frac{\sqrt[]{65}}{9}[/tex]120 100 temperature in °F 60 20 0 10 30 40 50 60 70 80 latitude in degrees North Add points that represent the predicted temperatures for each city on your scatter plot from the original cities. If you do not have a copy of your work from yesterday, you may choose to use the scatterplot above. Copy the data over or print a copy of the scatterplot here Scatterplot.pdf Upload a photo of your work in the space below. Upload Choose a File
Scatterplot is a simple graph that follows x and y coordinates.
Once you have the name of the cities, you can look up their latitude either using a printed map or online map, and that will be your x coordinate.
For your y coordinate, that will be the predicted temperature.
For example, the latitude of the Detroit is 42 degrees North (x coordinate) and has a temperature of 52 degree Fahrenheit (y coordinate), then we can have this plotted like this: (disregard the yellow line, it is only there as basis)
Another example: This is for Albuquerque. The latitude is 35.2 (x coordinate) and it's predicted temperature today is 73 degree Fahrenheit (y coordinate).
The red dot on the image above, that is where we will plot Albuquerque since it's latitude is 35.2 and its temperature is 73, as shown by the yellow lines. (Do not draw the yellow lines. It is only there for basis.)
You do the same with the rest of the cities using its corresponding latitude and predicted temperature today.
In the picture, point C is a point of tangency.158AEDA =DE=
we have that
If point C is a point of tangency
then
triangle ACD is a right triangle
so
Applying Pythagorean Theorem
DA^2=AC^2+CD^2
we have
AC=8 units
CD=15 units
substitute
DA^2=8^2+15^2
DA^2=64+225
DA^2=289
DA=17 unitsPart 2
Find DE
we have that
DA=DE+EA ------> by addition postulate theorem
we have
DA=17 units
EA=AC=8 units
substitute
17=8+DE
DE=9 unitsHello! I need some assistance with this homework question I have. The image is posted below Q2
Given the following question:
[tex](x-1)(3x+8)=0[/tex][tex]\begin{gathered} \mleft(x-1\mright)\mleft(3x+8\mright)=0 \\ (x-1)=0 \\ -1+1=0 \\ 0+1=1 \\ x=1 \\ \\ (3x+8)=0_{} \\ 8-8=0 \\ 0-8=-8 \\ 3x=-8 \\ 3x\div3=x \\ -8\div3=-\frac{8}{3} \\ x=-\frac{8}{3} \end{gathered}[/tex]Your answers are x = 1, and x = -8/3.
3АуWhat is the domain of the displayed function?*(1 Point)*(1-5, 5, -1, -5, 2, 1, 2, 5, 3, 1}}1-5. - 1, 2, 3){1, 4, 7, 8)15. 1. - 5)
Note that the domain of a relation is the set of all the values of the indeped
What are your thoughts? Is mathematics important in getting a good paid career?
Based on the statistics shown, we can see that 8 out of the 9 of the best-paying college majors are engineers, and in engineering, there is a lot of math involved, which means that math is important in getting a good-paid career.
Answer: mathematics is important in getting a good-paid career.
In the problem below, AABC AADC. Solve for x. Then, use that value to find the length of BC.
If the triangle ABC is congruent to triangle ADC, then the sides BC and DC are corresponding sides. So, we can formulate the following equation:
12x - 15 = 3x + 30
12x - 15 - 30 = 3x (Subtracting 30 from both sides of the equation)
-15-30 = 3x - 12x (Subtracting 12x from both sides of the equation)
-45 = -9x (Adding like terms)
-45/-9 = x (Dividing by -9 on both sides of the equation)
5 = x (Dividing)
So, x = 5
Replacing x=5 in the equation of side BC, we have:
BC = 12*(5) - 15
BC = 60 - 15 (Multiplying)
BC = 45 (Subtracting)
BC= 45.
Which expression represents the average of three test scores? O X+y+Z O 3(x+y+z) o **** X+y+Z 3 om ΧΟΣ 3
We need to find the expression that represents the average of three test scores
At first : the average = the sum of the data over the number of the data
We have 3 test scores : x , y and z
The sum of the scores = x + y + z
The number of the scores = 3
so, the average will be :
[tex]\frac{x+y+z}{3}[/tex]So, the answer is : ( x + y+ z )/3