If the number is between 0 and 1, and we are writing it in scientific notation, the exponent of the power of 10 is going to be smaller than 0 (that is a negative number for the exponent)
This is because the number of powers of ten are going to be part of a denominator.
For example, the number 0.001 which is between zero and 1 , can be written as:
1 divided by 1000. Notice then the 1000 value is in the denominator. powers of 10 in the denominator are represented always with negative exponents when written in scientific notation.
Anotther example is shown below:
[tex]0.0005=\frac{5}{10000}=\frac{5}{10^4}=5\, \, 10^{=4}[/tex]Again, the exponent of the power 10 will be a negative integer number in scientific notation.
which property of equality was used in this expression. 4y = 484y ÷ 4 = 48 ÷ 4
Explanation:
4y = 48
4y ÷ 4 = 48 ÷ 4
for a = b and c not equal to zero
a/c = b/c
This is a division property of equality.
4y ÷ 4 = 48 ÷ 4
we are dividing both sides by 4
This is also a division property of equality
Two cars traveled equal distences in different amounts of time. Car A travled the distence in 2 h, and car B traveled the distence in 1.5 h. Car B traveled 15 mph faster tha car A. ( the formula R×T=D, where R is the rate of speed, T is the time, and D is the distance can be used.) Enter your answer in the box. PLEASE HELP a
Let:
[tex]\begin{gathered} v_a=\text{Car A speed} \\ v_b=\text{Car B speed} \\ \text{ Since Car B traveled 15mph faster than Car A} \\ v_a=v_b-15 \end{gathered}[/tex]Using the formula provided:
[tex]\begin{gathered} R\times T=D \\ v_a\times T=D \\ (v_b-15)\times2=1.5v_b_{} \\ 2v_b-30=1.5v_b \\ \text{Solving for vb} \\ 0.5v_b=30 \\ v_b=60\text{mph} \end{gathered}[/tex][tex]v_a=60-15=45\text{mph}[/tex]I need help with the entire page , this is for my finals !!
The Solution:
Given:
[tex]y=16000+5500x[/tex]a.
The explanatory variable is the number of years (x).
b.
The salary (y) when the number of years is 12 years.
[tex]y=16000+5500(12)=\text{ \$}82000[/tex]c.
The annual salary when x = 6 years.
[tex]y=16000+5500(6)=\text{ \$}49000[/tex]d.
The residual for someone who has completed high school education for 6 years.
Residual = actual y value − predicted y value.
[tex]Residual=46000-49000=-\text{\$}3000[/tex]HELP ME PLEASEEEEEEEEEE
Answer: D) -2x - 7 < -15
greta cut a square from paper that measures 5 inches on each side. she then cut a square that measures 10 inches on each side what the difference in the area of the two squares?
Area of the square with side 5 inches = 5 x 5 = 25 square feet
Area of the square with side 10 inches = 10 x 10 = 100 square feet
Difference in area of the two squares = 100 - 25 = 75 square feet
S0, the solution is 75 square feet
Find two consecutive integers such that four times the greater integer is six less than five times the lesser integer
Find two consecutive integers such that four times the greater integer is six less than five times the lesser integer
Let
x -----> one integer
x+1 ----> second integer
4(x+1)=5x-6
solve for x
4x+4=5x+6
5x-4x=4-6
x=-2
so
x+1=-2+1=-1
the integers are -1 and -2Find the balance of an account where $3,300 was deposited 3 years ago, earning 4% interest.
SOLUTION
From the question
Principal, P = $3,300
Time, T = 3 years
Rate, R =4%
Using the simple interest formula
[tex]I=\frac{PRT}{100}[/tex]It follows:
[tex]\begin{gathered} I=\frac{3300\times4\times3}{100} \\ I=396 \end{gathered}[/tex]Therefore the total amount in the account is
[tex]\begin{gathered} A=3300+396 \\ A=3696 \end{gathered}[/tex]Therefore the total amount in the account is $3696
Emiko makes shibori scarves and sells them for $48 each on a website for handmade goods. The expression 48s represents the total price of buying & scarves What do the parts of the expression 48s represent? In the expression 48s s represents the number of scarves and 48 represents the price per scarf Buyers are charged a shipping fee of $4.75 for each scarf order. Which expression can you use to find the total price of a scarf order? 4.758 - 48 4.758 - 48 +8s +4.75
The total price of scarves is given by
48s.
After adding a shipping fee of $4.75, the expression to represent the total price of a scarf order is,
[tex]\text{Price}=48s+4.75[/tex]The fourth option is the correct answer
Answer: 48s + 4.75
Step-by-step explanation: just did the answer
Andres conducted a scientific experiment. For a certain time, thetemperature of a compound rose 21 degrees every 13 hours. Whatwas the rate, in degrees per hour, that the temperature of thecompound rose? Enter your answer as a whole number, properfraction, or mixed number in simplest form.
Given:
The temperature of a compound rose is 21 degrees every 13 hours.
Required:
Find the rate, in degrees per hour, that the temperature of the compound rose.
Write the answer as a whole number, proper fraction, or mixed number in simplest form.
Explanation:
Given that the temperature of a compound rose is 21 degrees every 13 hours.
So the rate of the temperature
[tex]\begin{gathered} =\frac{21}{13} \\ =1\frac{8}{13} \\ =1.615384 \end{gathered}[/tex]Final answer:
The rate of the temperature is
[tex]\frac{21}{13}=1\frac{8}{13}=1.615384[/tex]i need help with this please and simple explanation (question 5)
First thing is to find the coordinates for the two points
(-3,-2) and ( 0,2)
Then we can use the slope formula to determine the slope
m = ( y2-y1)/(x2-x1)
= ( 2 - -2) / ( 0 - -3)
= ( 2+2) / (0+3)
= 4/3
The slope is 4/3
You can also count how many you go up and then how many you go over to get from the left point to the right point.
We go up 4 and then right 3
4/3
The y intercept is where it crosses the y axis.
It crosses at y =2
The slope intercept form of the equation is
y = mx+b where m is the slope and b is the y intercept
y = 4/3x +2
Out of 200 people sampled, 170 had kids. Based on this, construct a 99% confidence interval for the true population proportion of people with kids.Give your answers as decimals, to three places
The sample proportion is calculated as:
[tex]p=\frac{170}{200}=0.85[/tex]The critical value for significance level = 1 - 0.99 = 0.01, from the z table is z = 2.3263
Therefore, the 99%confidence interval is computed as follows:
[tex]CI=(p-z_c\sqrt{\frac{p(1-p)}{n}},p+z_c\sqrt{\frac{p(1-p)}{n}})[/tex]Where:
p = 0.85
zc = 2.3263
n = 200
Substitute the values we have:
[tex]CI=(0.85-2.3263\sqrt{\frac{0.85(1-0.85)}{200}},0.85+2.3263\sqrt{\frac{0.85(1-0.85)}{200}})[/tex]Simplify:
[tex]\begin{gathered} CI=(0.85-0.0587,0.85+0.0587) \\ CI=(0.7913,0.9087) \end{gathered}[/tex]For 3 decimal places is (0.791, 0.909).
Answer: (0.791, 0.909)
The table shows how the cost of hiring a plumber depends on how long the worktakes. Give the rule in words describing the relationship between the hours workedand the cost.
Solution:
Given the table;
There is a linear relationship between cost of hiring a plumber and how long the work takes. This relationship is modelled as;
[tex]c\left(t\right)=25t+40[/tex]This shows that there is a fixed price of $40 charged and a price of $25 for each hour the work takes
Isabella's parents are starting acollege fund for her today, onher fifth birthday. Assumingthey make no additional depositsor withdrawals, if they want togive her 50 000 Brazilian Realon her eighteenth birthday,how much do they need to deposit now if the bank isoffering an interest rate of 5.5%,compounded monthly. Roundyour answer to the nearestwhole number.
Today Isabella is having her 5th birthday and her parents want to make one single deposit now so they can collect a total of 50000 Brazilian Real when she is 18.
The investment is thought to be for n=13 years.
The present value (PV) and the future value (FV) of the investment can be calculated by using the compound interest's formula:
[tex]FV=PV(1+\frac{r}{m})^{n\cdot m}[/tex]Where r is the interest rate (APR) offered by the bank, m is the number of compounding periods by each year. Since the compounding period is monthly, then m=12.
If we are given the final value and we want to calculate the present value, then the formula is:
[tex]PV=FV(1+\frac{r}{m})^{-n\cdot m}[/tex]Substituting:
[tex]PV=50000(1+\frac{0.055}{12})^{-13\cdot12}[/tex]Calculating:
[tex]\begin{gathered} PV=50000(1.0045833)^{-156} \\ PV=50000\cdot0.49 \\ PV=24499.59 \end{gathered}[/tex]Isabella's parents should deposit near 24500 Brazilian Reals today
factor x^4-5x^2+4 completely
Set
[tex]x^4-5x^2+4=0[/tex]Then, if y=x^2;
[tex]\begin{gathered} y=x^2 \\ \Rightarrow x^4-5x^2+4=y^2-5y+4=0 \\ \Rightarrow y^2-5y+4=0 \end{gathered}[/tex]Solve for y using the quadratic equation formula, as shown below
[tex]\begin{gathered} \Rightarrow y=\frac{-(-5)\pm\sqrt[]{(-5)^2-4\cdot1\cdot4}_{}}{2\cdot1}=\frac{5\pm\sqrt[]{25-16}}{2}=\frac{5\pm3}{2} \\ \Rightarrow y=4,1 \end{gathered}[/tex]Therefore, since y=x^2,
[tex]\begin{gathered} \Rightarrow x^2=4,x^2=1 \\ \Rightarrow x=\pm2,x=\pm1 \end{gathered}[/tex]Finally,
[tex]\Rightarrow x^4-5x^2+4=(x-2)(x+2)(x-1)(x+1)[/tex]The factored form of x^4-5x^2+4 is (x-2)(x+2)(x-1)(x+1)
how do we do this one brainly got it werong
The situation is drawn in the diagram below:
We are interested in knowing the speed of the boat (dx/dt) when h = 10 ft and dh/dt = 2 ft/s.
Applying the Pythagorean Theorem:
[tex]h^2=x^2+6^2[/tex]Differentiating with respect to the time:
[tex]2h\cdot\frac{dh}{dt}=2x\cdot\frac{dx}{dt}[/tex]Simplifying and solving:
[tex]\frac{dx}{dt}=\frac{h}{x}\cdot\frac{dh}{dt}[/tex]When h = 10, we can solve for x:
[tex]\begin{gathered} x^2=h^2-6^2=100-36=64 \\ \\ x=\sqrt{64}=8 \end{gathered}[/tex]Substitute this value of x:
[tex]\frac{dx}{dt}=\frac{10}{8}\cdot2\text{ ft/s}[/tex]Calculating:
[tex]\frac{dx}{dt}=\frac{5}{2}\text{ ft/s}[/tex]b. To calculate the rate of change of the angle, we use the tangent ratio as follows:
[tex]\tan\theta=\frac{x}{6}[/tex]If this trapezoid is moved through the(x+3, y-2), what will thecoordinates of D' be?translation
Given the point D = (1, 2), under the translation:
x ⇒ x + 3
y ⇒ y -2
the points D becomes:
D' = (1 + 3, 2 - 2) = (4, 0)
So the answer is D' = (4, 0).
Give a linear function for the car seat for an electrician to come to your house and work for three hours he charges a 95 flat fee to come to your house and 35 per hour he’s there to work
Just to come to your house, you have to pay him $95. Then,
[tex]C(t)=95+"Something"\text{.}[/tex]After he arrives, time passes and you have to pay him $35 per hour. If he works in your house for t hours, you must pay him
[tex]35+35+\ldots+35\text{ }\leftarrow\begin{cases}t\text{ times}\end{cases}[/tex]Then, "something" is 35*t.
AnswerThe linear function encoding the cost C for an electrician to come to your house and work for t hours is
[tex]C(t)=95+35t\text{.}[/tex]The answer is C.
In AABC, the measure of _C=90°, the measure of ZA=41°, and BC = 33 feet. Find thelength of AB to the nearest tenth of a foot.Answer:6.1
By Trigonometric Ratio,
[tex]undefined[/tex]A piecewise function f(x) is defined as shown.f(x) = StartLayout enlarged left-brace 1st Row 1st column negative five-fourths x + 90, 2nd column 0 less-than-or-equal-to x less-than 40 2nd row 1st column negative three-eighths x + 75, 2nd column 40 less-than-or-equal-to x less-than-or-equal-to 200 EndLayoutWhich table could be used to graph a piece of the function?
Given:
[tex]\begin{gathered} -\frac{5}{4}x+90,\text{ 0}\leq x<40 \\ -\frac{3}{8}x+75,40\leq x\leq200 \end{gathered}[/tex]Required:
Which table would be used to graph a piece of the function.
Explanation:
Here the function is broken at the three points x=0, x=40, x=200.
So we will choose that table in which the values of x are 0,40,200.
In this table, you can see the values of x are 0,40, and 200.
Final Answer:
The correct answer is
A and B are similar, If the perimeter of A is 51cm. Find the perimeter of B.(English isn't my native language. Please correct me if I have any grammatical mistakes.)
Answer:
The perimeter of B is 153 cm.
Explanation:
Given two similar shapes and:
• The internal diameter of A = 6 cm
,• The internal diameter of B = 18 cm
The ratio of the perimeters of two similar shapes is equal to the ratio of the length of corresponding sides.
[tex]\begin{gathered} \frac{\text{ Internal Diameter of A}}{\text{ Internal Diameter of B}}=\frac{\text{ Perimeter of A}}{\text{ Perimeter of B}} \\ \frac{6}{18}=\frac{51}{\text{ Perimeter of B}} \end{gathered}[/tex]We solve for the perimeter of B.
[tex]\begin{gathered} \frac{6}{6\times3}=\frac{51}{x} \\ \frac{1}{3}=\frac{51}{x} \\ x=51\times3 \\ x=153\text{ cm} \end{gathered}[/tex]The perimeter of B is 153 cm.
Which type of transformation is represented by the figures in the graph A. dilation and rotation B. Reflection and translation C. Reflection D. Rotation
To generate the image we need to perform a rotation. To perform a rotation every point on the function or figure must mantain the same distance of the center of rotation and move in a circle around it. We can see that the operation used was a rotation, because we can trace a circle between each point from the function to the image around the origin. The angle of rotation was 180 degrees.
Ann went bowling and got a score of 210 on her first game. On her second game, her score was 280. What was the percent of increase in her score on the second game?
ANSWER
33.33%
EXPLANATION
We have that her score on the first game was 210 and on her second game it was 280.
To find the percent of increase, we have to first find the difference between her first and second scores, then divide that by her first score and multiply by 100 (per cent).
Therefore, we have that the percent of increase is:
[tex]\begin{gathered} \frac{280-210}{210}\cdot100 \\ \frac{70}{210}\cdot100 \\ 33.33\text{ \%} \end{gathered}[/tex]That is the percent of increase.
Enter the value in the bank that completes the equation below
Given the equation;
[tex]4^5\cdot4^3=4^{\text{?}}[/tex]Note that the index powers of two numbers that are equal would be added together. That i;
[tex]\begin{gathered} 4^5\cdot4^3=4^{5+3} \\ 4^5\cdot4^3=4^8 \\ \text{Note that;} \\ (4\times4\times4\times4\times4)\cdot(4\times4\times4)=4\times4\times4\times4\times4\times4\times4\times4 \end{gathered}[/tex]ANSWER:
[tex]4^8[/tex]Be sure to answer all parts.Carry out each calculation and give the answer using the proper number of significant figures.b. 113.5 x 38 =
ANSWER:
4313
STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]113.5\times38[/tex]We solve as follows:
Therefore, the result is 4313.0
How do I solve this system of equation by graphing Y = x + 312x + y = -6
Let's pick a method to solve this system:
Let's try substitution:
So x= -9/13 y= 30/13
Ricardo thought it would be best to start making his own lunch to take to work instead of going outto eat and buying a meal. He usually spends $7 for the meal which also includes a soda. The lunch hemakes at home costs him $4 and he takes a refillable bottled water for his drink. How much does hesave after making his own lunch for 15 days?
he save $3 per day so in 15 days we would have saved $45
Sarah bought a new dress. She had a coupon for 35% off one item. If she saved $14, how much was the original price of the dress?
Percentage is expressed in terms of 100.
Let the original price of the dress be x. If there is a coupon of 35%, then the amount that was taken off the original price is
35/100 * x
= 0.35x
This is the same as the amount she saved. If the amount saved is $14, then
0.35x = 14
x = 14/0.35
x = 40
The original price of the dress is $40
The original price of the dress is $40.
Given in the question,
She had a coupon for 35% off one item.
Discount = 35%
she saved $14.
Let the original price of the dress be 'x.'
So, the percentage is expressed as 100
if she got 35% off, it meant,
= 35x/100
= 0.35x
Now, we will find the original price of the dress,
She saves $14.
original price = 14/0.35
x = $40
Therefore, the original price of the dress is $40.
To know more about percentage questions:
https://brainly.com/question/14092603
Convert from decimal degrees to degrees-minutes-seconds.Round to the nearest minute.
Given:
There are given that degree.
[tex]29.75^{\circ}[/tex]Explanation:
According to the question:
We need to convert the given degree to minutes.
Then,
From the given expression:
[tex]29.75^{\operatorname{\circ}}[/tex]Then,
[tex]29.75^{\operatorname{\circ}}=29^{\circ}+0.75^{\circ}[/tex]Then,
To convert the degrees to minutes, we need to multiply by 60.
So,
[tex]\begin{gathered} 29^{\circ}+0.75^{\circ}=29^{\circ}+0.75\times60 \\ =29^{\circ}+45^{\prime} \end{gathered}[/tex]Final answer:
Hence, the value of the given expre
please help me with this question , thank you so much Item 4 - find the missing part
the measure of the inscribed angle is half of the m
8 counters divided into 4 groups, has ? in each group
Explanation:
We have to divide the number of counters by the number of groups:
[tex]8\colon4=2[/tex]Answer:
Has 2 in each group